https://murray.cds.caltech.edu/api.php?action=feedcontributions&user=Liu&feedformat=atomMurray Wiki - User contributions [en]2022-09-25T21:10:32ZUser contributionsMediaWiki 1.37.2https://murray.cds.caltech.edu/index.php?title=Feb/Mar_2012_Meetings&diff=13708Feb/Mar 2012 Meetings2012-02-20T21:05:42Z<p>Liu: /* Mon, 5 Mar */</p>
<hr />
<div>I would like to meet with everyone sometime in the last week of Feb/first week of March. Please sign up for a time below (note that the slots are different lengths). __NOTOC__<br />
<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=50% |<br />
{| width=100% cellspacing=0 cellpadding=0<br />
|- bgcolor=yellow<br />
|<br />
<font color=blue> '''In Santa Barbara'''</font> (Vanessa, Ophelia, Dan, Emzo)<br />
==== Tue, 28 Feb ====<br />
* 4:00p - Dan (60m)<br />
* 5:00p - Ophelia (60m)<br />
<br />
==== Wed, 29 Feb ====<br />
* 10:00a - Vanessa (60m)<br />
* 3:30p - Open (60m)<br />
|}<br />
<hr><br />
<br />
==== Thu, 1 Mar ====<br />
* 3:00p - Biocircuits subgroup (Dan, Zach, Ophelia)<br />
* 5:00p - Stephanie (45m)<br />
* 5:45p - Necmiye (45m)<br />
* 6:30p - Open (60m)<br />
<hr><br />
<br />
==== Fri, 2 Mar ====<br />
* 9:00a - Open (60m)<br />
* 10:00a - Eugene Lavretsky (75m)<br />
* 11:15a - Hold, Eugene (45m)<br />
:<br />
* 12:00p - Group meeting<br />
* 1:15p - NCS subgroup (Mumu, Pavithra)<br />
* 3:00p - Pavithra (45m)<br />
* 3:45p - Andrea (60m)<br />
* 4:45p - Shaunak (45m)<br />
* 5:30p - Pete (60m)<br />
| width=50% |<br />
<br />
==== Mon, 5 Mar ====<br />
* 9:00a - Open (60m)<br />
* 10:00a - BE 150<br />
* 11:00a - Ufuk (45m)<br />
* 11:45a - Jun (45m)<br />
:<br />
* 1:00p - Scott Livingston (60m)<br />
* 2:00p - Mumu (60m)<br />
* 3:00p - Robotics subgroup (Pete, Andrea)<br />
* 4:30p - Enoch (60m)<br />
* 5:30p - Open (60m)<br />
* 6:30p - Open (60m)<br />
<hr><br />
<br />
==== Tue, 6 Mar ====<br />
* 9:00a - Open (60m)<br />
* 10:00a -Eric (60m)<br />
* 11:00a - Hold: CDS 90 (60m)<br />
<br />
* 2:00p - Hold: CDS 90 (60m)<br />
* 3:00p - Biocircuits subgroup (Enoch, Vanessa, Victoria)<br />
* 5:00p - iGEM<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Gabor_Orosz,_Feb_2012&diff=13655Gabor Orosz, Feb 20122012-02-17T17:14:05Z<p>Liu: /* 22 Feb (Wed) */</p>
<hr />
<div>Gabor Orosz, an Assistant Professor at U. Michigan, will be visiting Caltech on 21-22 Feb (Tue-Wed).<br />
<br />
=== Schedule ===<br />
<br />
==== 21 Feb (Tue) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|~10:00a|Marcella Gomez, meet in Steele library}}<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunchtime seminar: Gabor Orosz}}<br />
{{agenda item|1:00p|Richard and Marcella (109 Steele)}}<br />
{{agenda item|2:00p|Jongmin}}<br />
{{agenda item|3:00p|Biocircuits subgroup}}<br />
{{agenda item|5:00p|Paul Nguyen}}<br />
{{agenda end}}<br />
<br />
==== 22 Feb (Wed) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Jun}}<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunch}}<br />
{{agenda item|1:30p|Necmiye}}<br />
{{agenda item|2:15p|Marcella}}<br />
{{agenda item|3:00p|Depart for LAX}}<br />
{{agenda end}}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Gabor_Orosz,_Feb_2012&diff=13654Gabor Orosz, Feb 20122012-02-17T17:13:48Z<p>Liu: /* 22 Feb (Wed) */</p>
<hr />
<div>Gabor Orosz, an Assistant Professor at U. Michigan, will be visiting Caltech on 21-22 Feb (Tue-Wed).<br />
<br />
=== Schedule ===<br />
<br />
==== 21 Feb (Tue) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|~10:00a|Marcella Gomez, meet in Steele library}}<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunchtime seminar: Gabor Orosz}}<br />
{{agenda item|1:00p|Richard and Marcella (109 Steele)}}<br />
{{agenda item|2:00p|Jongmin}}<br />
{{agenda item|3:00p|Biocircuits subgroup}}<br />
{{agenda item|5:00p|Paul Nguyen}}<br />
{{agenda end}}<br />
<br />
==== 22 Feb (Wed) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Open}} Jun<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunch}}<br />
{{agenda item|1:30p|Necmiye}}<br />
{{agenda item|2:15p|Marcella}}<br />
{{agenda item|3:00p|Depart for LAX}}<br />
{{agenda end}}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Gabor_Orosz,_Feb_2012&diff=13644Gabor Orosz, Feb 20122012-02-16T10:15:29Z<p>Liu: /* 22 Feb (Wed) */</p>
<hr />
<div>Gabor Orosz, an Assistant Professor at U. Michigan, will be visiting Caltech on 21-22 Feb (Tue-Wed).<br />
<br />
=== Schedule ===<br />
<br />
==== 21 Feb (Tue) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|~10:00a|Marcella Gomez, meet in Steele library}}<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunchtime seminar: Gabor Orosz}}<br />
{{agenda item|1:00p|Richard and Marcella (109 Steele)}}<br />
{{agenda item|2:00p|Open}}<br />
{{agenda item|3:00p|Biocircuits subgroup}}<br />
{{agenda item|5:00p|Paul Nguyen}}<br />
{{agenda end}}<br />
<br />
==== 22 Feb (Wed) ====<br />
<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Open}}<br />
{{agenda item|11:00p|Seminar: Marta Kwiatkowska}}<br />
{{agenda item|12:00p|Lunch}}<br />
{{agenda item|1:30p|Necmiye}}<br />
{{agenda item|2:15p|Marcella}}<br />
{{agenda item|3:00p|CDS tea, Annenberg Loung}}<br />
{{agenda item|3:45p|Open}}<br />
{{agenda item|4:30p|Jun Liu}}<br />
{{agenda end}}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Group_Schedule,_Winter_2012&diff=13303Group Schedule, Winter 20122011-12-09T13:06:46Z<p>Liu: /* Week 1: 4-6 Jan */</p>
<hr />
<div>This page contains information about various upcoming events that are of interest to the group. __NOTOC__<br />
{| width=60%<br />
|- valign=top<br />
| width=50% |<br />
* [http://www.cds.caltech.edu/~murray/calendar.html Richard's calendar (travel)]<br />
| width=50% |<br />
* [[Group Schedule, Fall 2011]]<br />
|}<br />
<br />
The schedule for group and subgroup meetings is given below. Everyone should sign up for times to talk in the subgroup meetings.<br />
<br />
<font color=red><br />
==== Directions: ====<br />
* '''Biocircuits (Tue or Thu, 3-5 pm)''': graduate students should give 1 longer presentation per term + 1-2 additional research updates; postdocs, undergrads should give 1-2 research updates.<br />
* '''NCS (Wed, 4-6 pm)''': grad students should speak 2 times per term for 15-20 min (+ discussion), postdocs and undergrads at least once<br />
* '''Robotics (Wed, 4-6 pm)''': grad students and postdocs should speak 2 times per term for 15-20 min (+ discussion), undergrads at least once; will also do ad hoc updates<br />
* '''Group meeting talks (WThF, 12-1:15)''': postdocs and senior grad students (G4+) should feel free to sign up for a group meeting talk (biocircuit grad students: this can be in place of longer subgroup talk)<br />
</font><br />
<br />
<center><br />
'''Please sign up for at least one presentation in the first six weeks of the term.'''<br />
</center><br />
<br />
<font color=blue>Note that some of the meetings might need to shift, as noted; only sign up for those slots if you can make both times listed</font><br />
<br><br />
<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=30% |<br />
<br />
=== Week 1: 4-6 Jan ===<br />
'''NCS: 4 Jan (Wed), 4-6 pm'''<br />
* Jun Liu (15-20 min)<br />
* Open (15-20 min)<br />
* Project updates<br />
'''Group meeting: 5 Jan (Thu), 12-1:15'''<br />
* Ophelia<br />
'''Biocircuits: 5 Jan (Thu), 3-5 pm'''<br />
* Safety briefing (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
<hr><br />
Academic holiday, 2-3 Jan<br><br />
CDS quals, 6 Jan (RMM busy all day)<br />
| width=30% |<br />
<br />
=== Week 2: 9-13 Jan ===<br />
'''Robotics: 11 Jan (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Short research updates (5 min each)<br />
* <font color=blue>Might shift to Fri, 1-3 pm</font><br />
'''Biocircuits: 12 Jan (Thu), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
'''Group meeting: 13 Jan (Fri), 12-1:15 pm'''<br />
* Domitilla Del Vecchio (MIT)<br />
| width=30% |<br />
<br />
=== Week 3: 16-20 Jan ===<br />
'''Biocircuits: 17 Jan (Tue), 2-4 pm'''<br />
* Research presentation (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
* <font color=blue>Note time shift in day (to "regular" day)</font><br />
'''NCS: 18 Jan (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Project updates<br />
'''Group meeting: 19 Jan (Thu), 12-1:15'''<br />
* Naira Hovakimyan (UIUC)<br />
|- valign=top<br />
|<br />
<br />
=== Week 4: 23-27 Jan ===<br />
'''Biocircuits: 24 Jan (Tue), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
'''Group meeting: 25 Jan (Wed), 12-1:15'''<br />
* Necmiye<br />
'''Robotics: 25 Jan (Wed), 4-6 pm'''<br />
* Stephanie (15-20 min)<br />
* Open (15-20 min)<br />
* Short research updates (5 min each)<br />
* <font color=blue>Might shift to Fri, 1-3 pm</font><br />
|<br />
<br />
=== Week 5: 30 Jan - 3 Feb ===<br />
'''Biocircuits: 31 Jan (Tue), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Nikki(10-15 min)<br />
* Zach (10-15 min)<br />
* Lab updates<br />
'''NCS: 1 Feb (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Project updates<br />
'''Group meeting: 2 Feb (Thu), 12-1:15'''<br />
* Jongmin<br />
|<br />
<br />
=== Week 6: 6 Feb - 10 Feb ===<br />
'''Biocircuits: 7 Feb (Tue), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Paul (10-15 min)<br />
* Victoria (10-15 min)<br />
* Lab updates<br />
'''Group meeting: 8 Feb (Wed), 12-1:15'''<br />
* Andrea<br />
'''Robotics: 8 Feb (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Short research updates (5 min each)<br />
<br />
|- valign=top<br />
|<br />
<br />
=== Week 7: 13-17 Feb ===<br />
'''NCS: 15 Feb (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Project updates<br />
'''Group meeting: 16 Feb (Thu), 12-1:15'''<br />
* Open<br />
'''Biocircuits: 16 Feb (Thu), 3-5 pm'''<br />
* Safety briefing (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
* <font color=blue>Note change in day</font><br />
|<br />
<br />
=== Week 8: 20-24 Feb ===<br />
'''Biocircuits: 21 Feb (Tue), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
'''Robotics: 22 Feb (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Short research updates (5 min each)<br />
'''Group meeting: 23 Feb (Thu), 12-1:15'''<br />
* Hold: possible job talk<br />
|<br />
<br />
=== Week 9: 27 Feb - 2 Mar ===<br />
'''Biocircuits: 28 Feb (Tue), 3-5 pm'''<br />
* Safety briefing (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
* <font color=blue>Will probably shift to 2 Mar, 3-5 pm</font><br />
'''NCS: 29 Feb (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Project updates<br />
* <font color=blue>Will probably shift to 2 Mar, 1-3 pm</font><br />
'''Group meeting: 2 Mar (Fri), 12-1:15'''<br />
* Open<br />
|- valign=top<br />
|<br />
<br />
=== Week 10: 5-9 Mar ===<br />
'''Biocircuits: 6 Mar (Tue), 3-5 pm'''<br />
* Research presentation (30-40 min) <br />
* Research update (10-15 min)<br />
* Research update (10-15 min)<br />
* Lab updates<br />
'''Robotics: 7 Mar (Wed), 4-6 pm'''<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* Short research updates (5 min each)<br />
'''Group meeting: 9 Mar (Fri), 12-1:15'''<br />
* Hold: possible job talk<br />
|<br />
<br />
=== Week 11: 12-16 Mar ===<br />
Finals week; Richard out of town<br />
|<br />
=== Week 12: 19-23 Mar ===<br />
Spring break; Richard out of town<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Group_Schedule,_Fall_2011&diff=12966Group Schedule, Fall 20112011-09-19T23:31:14Z<p>Liu: /* Week 3: 10-14 Oct */</p>
<hr />
<div>This page contains information about various upcoming events that are of interest to the group. __NOTOC__<br />
{| width=60%<br />
|- valign=top<br />
| width=50% |<br />
* [http://www.cds.caltech.edu/~murray/calendar.html Richard's calendar (travel)]<br />
| width=50% |<br />
* [[Group Schedule, Summer 2011]]<br />
|}<br />
<br />
The schedule for group and subgroup meetings is given below. Everyone should sign up for times to talk in the subgroup meetings.<br />
* Biocircuits: everyone should speak 2-3 times per term<br />
* NCS/robotics: grad student should speak 2 times per term, postdocs and undergrads at least once<br />
* Students/postdocs applying for jobs: if you want to give a "job talk" in group meeting, let me know <br />
Note that some of the meetings might need to shift; only sign up for those slots if you can make both times listed<br />
<br><br />
<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=30% |<br />
=== Week 1: 26-30 Sep ===<br />
27 Sep (Tue), 1-3 pm: Biocircuits<br />
* Paul Nguyen<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
28 Sep (Wed), 12 pm: Group meeting <br />
* Hold: Pavrithra Prabhakar<br />
28 Sep (Wed), 1-3 pm: NCS<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
| width=30% |<br />
<br />
=== Week 2: 3-7 Oct ===<br />
3 Oct (Mon), 12 pm: Group meeting <br />
* Dan Siegal-Gaskins<br />
4 Oct (Tue), 1-3 pm; Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
5 Oct (Wed), 1-3 pm: Robotics<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* ''Note'': might shift to 3:30-5 pm<br />
<hr><br />
ARO synthetic biology workshop Thu-Fri<br />
* Possible lab tours on Fri morning<br />
| width=30% |<br />
<br />
=== Week 3: 10-14 Oct ===<br />
No group meeting <br />
<br />
11 Oct (Tue), <font color=blue>12:30-2 pm</font>: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
12 Oct (Wed), 1-3 pm: NCS<br />
* Jun (15-20 min)<br />
* Ufuk (15-20 min)<br />
<hr><br />
Rob Wood visiting on 11 Oct (Tue)<br />
<br />
Boeing Annual Review on 12 Oct (Wed)<br />
|- valign=top<br />
|<br />
<br />
=== Week 4: 17-21 Oct ===<br />
18 Oct (Tue), 1-3 pm: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
19 Oct (Wed), 12 pm: Group meeting <br />
* Hold: job talk<br />
19 Oct (Wed), 1-3 pm: Robotics<br />
* Shuo (15-20 min)<br />
* Open (15-20 min)<br />
|<br />
<br />
=== Week 5: 24-28 Oct ===<br />
25 Oct (Tue), <font color=blue>10:30-12</font>: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* ''Note'': might shift to 12:30-2 pm<br />
26 Oct (Wed), 12 pm: Group meeting <br />
* Hold: job talk<br />
26 Oct (Wed), <font color=blue>3:30-5 pm</font>: NCS<br />
* Mumu (15-20 min)<br />
* Open (15-20 min)<br />
|<br />
<br />
=== Week 6: 31 Oct - 4 Nov ===<br />
1 Nov (Tue), 1-3 pm; Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
2 Nov (Wed), 12 pm: Group meeting <br />
* Hold: Qi Song (incoming visitor)<br />
2 Nov (Wed), 1-3 pm: Robotics<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
|- valign=top<br />
|<br />
=== Week 7: 7-11 Nov ===<br />
<font color=blue>7 Nov (Mon), 12:30-2:30 pm</font>: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
10 Nov (Thu), 12 pm: Group meeting <br />
* Hold: job talk<br />
<font color=blue>10 Nov (Thu), 1-3 pm</font>: NCS<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
* ''Note'': Might move to Mon, 2:30-4 pm <br />
<hr><br />
Richard out of town Tue-Wed, possibly Thu-Fri<br />
|<br />
<br />
=== Week 8: 14-18 Nov ===<br />
No group meeting<br />
<br />
<font color=blue>14 Nov (Mon), 12:30-2 pm</font>: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
<font color=blue>18 Nov (Thu), 4-5:30 pm</font>: Robotics<br />
* Shuo (15-20 min)<br />
* Open (15-20 min)<br />
<hr><br />
Richard out of town Tue-Wed<br />
<br />
MuSyC workshop/review Wed-Fri<br />
|<br />
<br />
=== Week 9: 21-25 Nov ===<br />
22 Nov (Tue), <font color=blue>12:30-2 pm</font>: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
23 Nov (Wed), 12 pm: group meeting<br />
* Dionysios<br />
23 Nov (Wed), 1-3 pm: NCS<br />
* Mumu (15-20 min)<br />
* Open (15-20 min)<br />
<hr><br />
Thanksgiving holiday: Thu-Fri<br />
|- valign=top<br />
|<br />
<br />
=== Week 10: 28 Nov - 2 Dec ===<br />
29 Nov (Tue), 1-3 pm: Biocircuits<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
* Open (10-15 min)<br />
30 Nov (Wed), 12 pm: Group meeting <br />
* Hold: job talk<br />
30 Nov (Wed), 1-3 pm: Robotics<br />
* Open (15-20 min)<br />
* Open (15-20 min)<br />
|<br />
<br />
=== Week 11: 5-9 Dec ===<br />
Final weeks week, Richard out of town<br />
<br />
No group or subgroup meetings<br />
|<br />
=== Week 12: 12-16 Dec ===<br />
CDC week, Richard (probably) in town<br />
<br />
Group and subgroup meetings TBD<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Group_Schedule,_Summer_2011&diff=12731Group Schedule, Summer 20112011-06-20T18:32:35Z<p>Liu: /* 4-8 Jul */</p>
<hr />
<div>__NOTOC__<br />
This page contains information about various upcoming events that are of interest to the group.<br />
{| width=60%<br />
|- valign=top<br />
| width=50% |<br />
* [http://www.cds.caltech.edu/~murray/calendar.html Richard's calendar (travel)]<br />
| width=50% |<br />
* [[Group Schedule, Spring 2011]]<br />
|}<br />
<br />
=== Summer Schedule ===<br />
<br />
{| border=1 width=100%<br />
|- valign=top<br />
| '''Week'''<br />
| '''Mini-group meetings'''<br />
| '''Group meeting'''<br />
| '''Other'''<br />
|- valign=top<br />
|<br />
===== 13-17 Jun =====<br />
|<br />
None<br />
| <br />
None<br />
| <br />
RMM out all week<br />
|- valign=top<br />
|<br />
===== 20-24 Jun =====<br />
|<br />
* iGEM: Mon @ 9:30<br />
* SURF meetings, cycle 0: (sign on at [[SURF 2011]] page)<br />
* NCS: Tue, 1-2:30 pm<br />
** Speaker 1: Necmiye (discussion)<br />
** Speaker 2: Linlin<br />
|<br />
Tue @ 12: Necmiye<br />
|<br />
RMM out 22-24 Jun<br />
|- valign=top<br />
|<br />
<br />
===== 27 Jun - 1 Jul =====<br />
|<br />
* iGEM: Mon, <font color=blue>9:30a-10:30a</font><br />
* Robotics: Mon, 1-3 pm<br />
** Speaker 1: Sawyer<br />
** Speaker 2: Sandeep<br />
* Biocircuits: Tue, 9a-2p<br />
** Overview presentations (all; 10 min each)<br />
** Lunch will be provided<br />
* SURF meetings, cycle 1: Tue pm<br />
** 4:00 pm: open<br />
** 4:30 pm: open<br />
** 5:00 pm: open<br />
** 5:30 pm: open<br />
** 6:00 pm: open<br />
| <br />
Mon @ 12: Nils Napp<br />
|<br />
* Nils Napp visiting<br />
* RMM out 29 Jun-1 Jul (ACC)<br />
|- valign=top<br />
|<br />
<br />
===== 4-8 Jul =====<br />
|<br />
* Biocircuits: Tue, 10-12<br />
** Speaker 1: Marcella<br />
** Speaker 2: Joe<br />
** Speaker 3: open<br />
* iGEM: Tue, <font color=blue>5:30-6:30p</font><br />
* NCS: Thu, 1-3 pm<br />
** Speaker 3: Scott Livingston<br />
** Speaker 4: Jun Liu<br />
* SURF meetings, cycle 1: Thu pm<br />
** 3:00 pm: open<br />
** 3:30 pm: open<br />
** 4:00 pm: Klavdia and Sawyer<br />
** 4:30 pm: open<br />
** 5:00 pm: open<br />
<br />
| <br />
Tue @ 12: Henrik Sandberg<br />
|<br />
* Institute holiday on Mon<br />
* Eric Colinet visiting on 5 Jul<br />
* Henrik Sandberg visiting 3-9 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 11-15 Jul =====<br />
|<br />
* iGEM: Mon, <font color=blue>9:30a-10:30a</font><br />
* Robotics: <font color=blue>Wed</font>, 1p-3p<br />
** Speaker 3: Shuo<br />
** Speaker 4: Andrea<br />
* Biocircuits: <font color=blue>Thu</font>, 10a-12p<br />
** Speaker 4: Ophelia<br />
** Speaker 5: open<br />
** iGEM presentation (30 min)<br />
* SURF meetings, cycle 2: Thu, pm<br />
** 3:00 pm: open<br />
** 3:30 pm: open<br />
** 4:00 pm: open<br />
** 4:30 pm: open<br />
| <br />
<font color=blue>Thu</font> @ 12: Speaker TBD <br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 18-22 Jul =====<br />
|<br />
* SURF meetings, cycle 2: Thu pm<br />
** 2:30p: open<br />
** 3:00p: open<br />
** 3:30p: open<br />
** 4:00p: Klavdia and Sawyer<br />
** 4:30p: open<br />
* iGEM: Thu, 5-6p<br />
* Biocircuits: Fri, 10a-12p<br />
** Speaker 6: Ye Yuan<br />
** Speaker 7: Dionysios<br />
** SURF 1: Paul<br />
* Robotics: Fri, 1p-3p<br />
** Speaker 5: pete<br />
** SURF 1: Magnus<br />
** SURF 2: Stephanie<br />
* NCS: Fri, 3p-5p<br />
** Speaker 5: Mumu<br />
** Speaker 6: Ufuk<br />
** SURF 1: Petter<br />
| <br />
Fri @ 12: Josh Michener<br />
|<br />
* RMM out 18-21 Jul am<br />
* Josh Michener visiting 22 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 25-29 Jul =====<br />
|<br />
| <br />
|<br />
* RMM out 25-29 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 1-5 Aug =====<br />
|<br />
* iGEM: Thu, 5-6 pm<br />
* Biocircuits: Fri, 10a-12p<br />
** Speaker 8: Marcella<br />
** SURF 2: Ishan<br />
** SURF 3: Arjun<br />
* NCS: Fri, 1p-3p<br />
** Speaker 7: Scott Livingston<br />
** Speaker 8: Eric<br />
** SURF 2: Yuchen<br />
* SURF meetings, cycle 3: Fri, pm<br />
** 3:00p: Klavdia and Sawyer<br />
** 3:30p: open<br />
** 4:00p: open<br />
** 4:30p: open<br />
** 5:00p: open<br />
| <br />
Fri @ 12: speaker TBD<br />
|<br />
* RMM out 1-4 Aug<br />
|- valign=top<br />
|<br />
<br />
===== 8-12 Aug =====<br />
|<br />
* Robotics: Tue, 1p-3p<br />
** Speaker 6: open<br />
** SURF 3: Klavdia<br />
* SURF meetings, cycle 3: Tue, pm<br />
** 3:00p: open<br />
** 4:30p: open<br />
** 4:00p: open<br />
** 5:30p: open<br />
** 6:00p: open<br />
* Biocircuits: Thu, 10a-12p<br />
** Speaker 9: Jongmin<br />
** Speaker 10: Shaunak<br />
** SURF 4: Keshav<br />
* iGEM: Thu, 5p-6p<br />
| <br />
Thu @ 12: speaker TBD<br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 15-19 Aug =====<br />
|<br />
| <br />
|<br />
RMM out 15-19 Aug<br />
|- valign=top<br />
|<br />
<br />
===== 22-26 Aug =====<br />
|<br />
* iGEM: Mon, <font color=blue>9a-10a</font><br />
* Biocircuits: Mon, 10a-12p<br />
** Speaker 11: open<br />
** Speaker 12: Enoch Yeung<br />
** Speaker 13: open<br />
* Robotics: Mon, 1p-3p<br />
** Speaker 7: open<br />
** Speaker 8: open<br />
* NCS: Mon, 3p-5p<br />
** Speaker 9: Linlin<br />
** Speaker 10: Necmiye<br />
| <br />
Tue @ 12: speaker TBD<br />
|<br />
RMM out: 25 Aug (pm) - 1 Sep (pm)<br />
|- valign=top<br />
|<br />
<br />
===== 29 Aug - 2 Sep =====<br />
|<br />
* Robotics: Thu, 1-3p<br />
** Speaker 9: Shuo<br />
** Speaker 10: Pete<br />
* NCS: Thu, 3-5p<br />
** Speaker 11: Asghar<br />
** Speaker 12: Eric<br />
* iGEM: Thu, 5p-6p<br />
* Biocircuits; Fri, 10a-12p<br />
** Speaker 14: Ophelia<br />
** Speaker 15: open<br />
** Speaker 16: open<br />
<br />
| <br />
Fri @ 12p (tentative): speaker TBD <br />
|<br />
* RMM out: 25 Aug (pm) - 1 Sep (pm)<br />
|- valign=top<br />
|<br />
<br />
===== 5-9 Sep =====<br />
|<br />
| <br />
|<br />
* RMM out, 5-9 Sep<br />
|- valign=top<br />
|<br />
===== 12-16 Sep =====<br />
|<br />
* Biocircuits: Tue, 10a-12p<br />
** Speaker 17: open<br />
** Speaker 18: open<br />
** Speaker 19: open<br />
* NCS: Wed, 1p-3p<br />
** Speaker 13: Mumu<br />
** Speaker 14: Ufuk<br />
| <br />
Tue @ 12p: speaker TBD<br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 19-23 Sep =====<br />
|<br />
* Robotics: Mon, 1p-3p<br />
** Speaker 11: Asghar<br />
** Speaker 12: Andrea<br />
* Biocircuits: Tue, 10a-12p<br />
** Speaker 20: open<br />
** Speaker 21: Enoch Yeung<br />
** Speaker 22: open<br />
| <br />
Tue @ 12p: speaker TBD<br />
|<br />
RMM out, 20 Sep (pm) to 23 Sep<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Group_Schedule,_Summer_2011&diff=12730Group Schedule, Summer 20112011-06-20T18:31:15Z<p>Liu: /* 20-24 Jun */</p>
<hr />
<div>__NOTOC__<br />
This page contains information about various upcoming events that are of interest to the group.<br />
{| width=60%<br />
|- valign=top<br />
| width=50% |<br />
* [http://www.cds.caltech.edu/~murray/calendar.html Richard's calendar (travel)]<br />
| width=50% |<br />
* [[Group Schedule, Spring 2011]]<br />
|}<br />
<br />
=== Summer Schedule ===<br />
<br />
{| border=1 width=100%<br />
|- valign=top<br />
| '''Week'''<br />
| '''Mini-group meetings'''<br />
| '''Group meeting'''<br />
| '''Other'''<br />
|- valign=top<br />
|<br />
===== 13-17 Jun =====<br />
|<br />
None<br />
| <br />
None<br />
| <br />
RMM out all week<br />
|- valign=top<br />
|<br />
===== 20-24 Jun =====<br />
|<br />
* iGEM: Mon @ 9:30<br />
* SURF meetings, cycle 0: (sign on at [[SURF 2011]] page)<br />
* NCS: Tue, 1-2:30 pm<br />
** Speaker 1: Necmiye (discussion)<br />
** Speaker 2: Linlin<br />
|<br />
Tue @ 12: Necmiye<br />
|<br />
RMM out 22-24 Jun<br />
|- valign=top<br />
|<br />
<br />
===== 27 Jun - 1 Jul =====<br />
|<br />
* iGEM: Mon, <font color=blue>9:30a-10:30a</font><br />
* Robotics: Mon, 1-3 pm<br />
** Speaker 1: Sawyer<br />
** Speaker 2: Sandeep<br />
* Biocircuits: Tue, 9a-2p<br />
** Overview presentations (all; 10 min each)<br />
** Lunch will be provided<br />
* SURF meetings, cycle 1: Tue pm<br />
** 4:00 pm: open<br />
** 4:30 pm: open<br />
** 5:00 pm: open<br />
** 5:30 pm: open<br />
** 6:00 pm: open<br />
| <br />
Mon @ 12: Nils Napp<br />
|<br />
* Nils Napp visiting<br />
* RMM out 29 Jun-1 Jul (ACC)<br />
|- valign=top<br />
|<br />
<br />
===== 4-8 Jul =====<br />
|<br />
* Biocircuits: Tue, 10-12<br />
** Speaker 1: Marcella<br />
** Speaker 2: Joe<br />
** Speaker 3: open<br />
* iGEM: Tue, <font color=blue>5:30-6:30p</font><br />
* NCS: Thu, 1-3 pm<br />
** Speaker 3: Scott Livingston<br />
** Speaker 4: Linlin<br />
* SURF meetings, cycle 1: Thu pm<br />
** 3:00 pm: open<br />
** 3:30 pm: open<br />
** 4:00 pm: Klavdia and Sawyer<br />
** 4:30 pm: open<br />
** 5:00 pm: open<br />
<br />
| <br />
Tue @ 12: Henrik Sandberg<br />
|<br />
* Institute holiday on Mon<br />
* Eric Colinet visiting on 5 Jul<br />
* Henrik Sandberg visiting 3-9 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 11-15 Jul =====<br />
|<br />
* iGEM: Mon, <font color=blue>9:30a-10:30a</font><br />
* Robotics: <font color=blue>Wed</font>, 1p-3p<br />
** Speaker 3: Shuo<br />
** Speaker 4: Andrea<br />
* Biocircuits: <font color=blue>Thu</font>, 10a-12p<br />
** Speaker 4: Ophelia<br />
** Speaker 5: open<br />
** iGEM presentation (30 min)<br />
* SURF meetings, cycle 2: Thu, pm<br />
** 3:00 pm: open<br />
** 3:30 pm: open<br />
** 4:00 pm: open<br />
** 4:30 pm: open<br />
| <br />
<font color=blue>Thu</font> @ 12: Speaker TBD <br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 18-22 Jul =====<br />
|<br />
* SURF meetings, cycle 2: Thu pm<br />
** 2:30p: open<br />
** 3:00p: open<br />
** 3:30p: open<br />
** 4:00p: Klavdia and Sawyer<br />
** 4:30p: open<br />
* iGEM: Thu, 5-6p<br />
* Biocircuits: Fri, 10a-12p<br />
** Speaker 6: Ye Yuan<br />
** Speaker 7: Dionysios<br />
** SURF 1: Paul<br />
* Robotics: Fri, 1p-3p<br />
** Speaker 5: pete<br />
** SURF 1: Magnus<br />
** SURF 2: Stephanie<br />
* NCS: Fri, 3p-5p<br />
** Speaker 5: Mumu<br />
** Speaker 6: Ufuk<br />
** SURF 1: Petter<br />
| <br />
Fri @ 12: Josh Michener<br />
|<br />
* RMM out 18-21 Jul am<br />
* Josh Michener visiting 22 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 25-29 Jul =====<br />
|<br />
| <br />
|<br />
* RMM out 25-29 Jul<br />
|- valign=top<br />
|<br />
<br />
===== 1-5 Aug =====<br />
|<br />
* iGEM: Thu, 5-6 pm<br />
* Biocircuits: Fri, 10a-12p<br />
** Speaker 8: Marcella<br />
** SURF 2: Ishan<br />
** SURF 3: Arjun<br />
* NCS: Fri, 1p-3p<br />
** Speaker 7: Scott Livingston<br />
** Speaker 8: Eric<br />
** SURF 2: Yuchen<br />
* SURF meetings, cycle 3: Fri, pm<br />
** 3:00p: Klavdia and Sawyer<br />
** 3:30p: open<br />
** 4:00p: open<br />
** 4:30p: open<br />
** 5:00p: open<br />
| <br />
Fri @ 12: speaker TBD<br />
|<br />
* RMM out 1-4 Aug<br />
|- valign=top<br />
|<br />
<br />
===== 8-12 Aug =====<br />
|<br />
* Robotics: Tue, 1p-3p<br />
** Speaker 6: open<br />
** SURF 3: Klavdia<br />
* SURF meetings, cycle 3: Tue, pm<br />
** 3:00p: open<br />
** 4:30p: open<br />
** 4:00p: open<br />
** 5:30p: open<br />
** 6:00p: open<br />
* Biocircuits: Thu, 10a-12p<br />
** Speaker 9: Jongmin<br />
** Speaker 10: Shaunak<br />
** SURF 4: Keshav<br />
* iGEM: Thu, 5p-6p<br />
| <br />
Thu @ 12: speaker TBD<br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 15-19 Aug =====<br />
|<br />
| <br />
|<br />
RMM out 15-19 Aug<br />
|- valign=top<br />
|<br />
<br />
===== 22-26 Aug =====<br />
|<br />
* iGEM: Mon, <font color=blue>9a-10a</font><br />
* Biocircuits: Mon, 10a-12p<br />
** Speaker 11: open<br />
** Speaker 12: Enoch Yeung<br />
** Speaker 13: open<br />
* Robotics: Mon, 1p-3p<br />
** Speaker 7: open<br />
** Speaker 8: open<br />
* NCS: Mon, 3p-5p<br />
** Speaker 9: Linlin<br />
** Speaker 10: Necmiye<br />
| <br />
Tue @ 12: speaker TBD<br />
|<br />
RMM out: 25 Aug (pm) - 1 Sep (pm)<br />
|- valign=top<br />
|<br />
<br />
===== 29 Aug - 2 Sep =====<br />
|<br />
* Robotics: Thu, 1-3p<br />
** Speaker 9: Shuo<br />
** Speaker 10: Pete<br />
* NCS: Thu, 3-5p<br />
** Speaker 11: Asghar<br />
** Speaker 12: Eric<br />
* iGEM: Thu, 5p-6p<br />
* Biocircuits; Fri, 10a-12p<br />
** Speaker 14: Ophelia<br />
** Speaker 15: open<br />
** Speaker 16: open<br />
<br />
| <br />
Fri @ 12p (tentative): speaker TBD <br />
|<br />
* RMM out: 25 Aug (pm) - 1 Sep (pm)<br />
|- valign=top<br />
|<br />
<br />
===== 5-9 Sep =====<br />
|<br />
| <br />
|<br />
* RMM out, 5-9 Sep<br />
|- valign=top<br />
|<br />
===== 12-16 Sep =====<br />
|<br />
* Biocircuits: Tue, 10a-12p<br />
** Speaker 17: open<br />
** Speaker 18: open<br />
** Speaker 19: open<br />
* NCS: Wed, 1p-3p<br />
** Speaker 13: Mumu<br />
** Speaker 14: Ufuk<br />
| <br />
Tue @ 12p: speaker TBD<br />
|<br />
|- valign=top<br />
|<br />
<br />
===== 19-23 Sep =====<br />
|<br />
* Robotics: Mon, 1p-3p<br />
** Speaker 11: Asghar<br />
** Speaker 12: Andrea<br />
* Biocircuits: Tue, 10a-12p<br />
** Speaker 20: open<br />
** Speaker 21: Enoch Yeung<br />
** Speaker 22: open<br />
| <br />
Tue @ 12p: speaker TBD<br />
|<br />
RMM out, 20 Sep (pm) to 23 Sep<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Elbert_Macau,_June_2011&diff=12577Elbert Macau, June 20112011-06-01T18:30:10Z<p>Liu: /* 2 Jun (Thu) */</p>
<hr />
<div>Elbert Macau will be visiting CDS on 1-3 Jun and is interested in learning more about research in CDS. Elbert is a professor at National Institute for Space Research, Brazil, working for the Laboratory for Applied Mathematics and Control (http://www.lac.inpe.br). His research group in working on collaborative cooperative control and synchronization in complex networks.<br />
<br />
Elbert will have a desk in 124 Steele during his visit. Please sign up for a time to meet with him below.<br />
<br />
{| border=1 width=100%<br />
|- valign=top<br />
| width=30% |<br />
==== 1 Jun (Wed) ====<br />
* Arrive at Caltech around 2 pm<br />
* 2 pm: Richard<br />
* 3 pm: CDS tea<br />
* 4 pm: Meet with Ashley Moore, 114 Steele<br />
| width=30% |<br />
<br />
==== 2 Jun (Thu) ====<br />
* 12 pm: Murray group meeting, 114 Steele<br />
* 1 pm: Meet with Jun Liu, 114 Steele<br />
| width=30% |<br />
<br />
==== 3 Jun (Fri) ====<br />
* (RMM at UCLA)<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Elbert_Macau,_June_2011&diff=12576Elbert Macau, June 20112011-06-01T18:29:51Z<p>Liu: /* 2 Jun (Thu) */</p>
<hr />
<div>Elbert Macau will be visiting CDS on 1-3 Jun and is interested in learning more about research in CDS. Elbert is a professor at National Institute for Space Research, Brazil, working for the Laboratory for Applied Mathematics and Control (http://www.lac.inpe.br). His research group in working on collaborative cooperative control and synchronization in complex networks.<br />
<br />
Elbert will have a desk in 124 Steele during his visit. Please sign up for a time to meet with him below.<br />
<br />
{| border=1 width=100%<br />
|- valign=top<br />
| width=30% |<br />
==== 1 Jun (Wed) ====<br />
* Arrive at Caltech around 2 pm<br />
* 2 pm: Richard<br />
* 3 pm: CDS tea<br />
* 4 pm: Meet with Ashley Moore, 114 Steele<br />
| width=30% |<br />
<br />
==== 2 Jun (Thu) ====<br />
* 12 pm: Murray group meeting, 114 Steele<br />
* 1 pm: Jun Liu, 114 Steele<br />
| width=30% |<br />
<br />
==== 3 Jun (Fri) ====<br />
* (RMM at UCLA)<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=June_2011_meetings&diff=12567June 2011 meetings2011-05-31T18:07:25Z<p>Liu: /* 8 Jun (Wed) */</p>
<hr />
<div>__NOTOC__<br />
{| border=1 width=100%<br />
|- valign=top<br />
| width=20% |<br />
<br />
| width=20% |<br />
<br />
| width=20% |<br />
==== 1 Jun (Wed) ====<br />
* 9:15a - Ye <br />
* 10:00a - Matanya<br />
* 11:00a - Marcella<br />
* 1:00p - Anu<br />
* 3:00p - CDS tea<br />
* 4:00p - Fei Y<br />
* 5:00p - (Shuo; lab stuff)<br />
* 5:30p - Dionysios<br />
* 6:30p - Shaunak<br />
| width=20% |<br />
==== 2 Jun (Thu) ====<br />
* 10:00a - Biocircuits<br />
* 12:00p - Group meeting<br />
* 5:30p - Necmiye<br />
| width=20% |<br />
==== 3 Jun (Fri) ====<br />
* UCLA<br />
* BE BBQ<br />
|- valign=top<br />
| width=20% |<br />
==== 6 Jun (Mon) ====<br />
* 10:00a - Vanessa<br />
* 11:00a - Henry J<br />
* 12:30p - Robotics<br />
* 5:30p - Andrea<br />
* 6:30p - Ophelia<br />
| width=20% |<br />
<br />
==== 7 Jun (Tue) ====<br />
* 10:00a - NCS<br />
* 12:00p - Group meeting<br />
* 3:30p - Scott Livingston<br />
* 4:30p - Aneesh<br />
* 5:30p - Ufuk<br />
* 6:30p - Open<br />
| width=20% |<br />
<br />
==== 8 Jun (Wed) ====<br />
* 9:30a - Eric<br />
* 10:30a - Mumu<br />
* 11:30a - Open<br />
* 1:00p - Open<br />
* 2:00p - Emzo<br />
* 3:00p - CDS tea<br />
* 5:30p - Jun Liu<br />
* 6:30p - Open<br />
* 7:30p - Open<br />
| width=20% |<br />
<br />
==== 9 Jun (Thu) ====<br />
* 11:30a - Open<br />
* 1:00p - Open<br />
* 2:00p - Open<br />
* 3:00p - CDS 90 <br />
* 4:30p - Enoch Yeung <br />
* 5:30p - Open<br />
* 6:30p - Open<br />
| width=20% |<br />
<br />
==== 10 Jun (Fri) ====<br />
* 5:30p - Open<br />
|}</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12514CDS 140b, Spring 20112011-05-12T05:03:51Z<p>Liu: /* Announcements */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 11 May 2011: Homework #4 posted; due 31 May 2011<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Periodically Perturbed Systems<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Perturbation.pdf Notes on Perturbation]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]<br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|- valign=top<br />
| 19 May <br> 24 May <br />
| Final Project Presentations<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12513CDS 140b, Spring 20112011-05-12T04:51:28Z<p>Liu: /* Announcements */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 11 May 2011: Homework #4 posted; due 26 May 2011<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Periodically Perturbed Systems<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Perturbation.pdf Notes on Perturbation]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]<br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|- valign=top<br />
| 19 May <br> 24 May <br />
| Final Project Presentations<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12512CDS 140b, Spring 20112011-05-12T04:40:50Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Periodically Perturbed Systems<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Perturbation.pdf Notes on Perturbation]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]<br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|- valign=top<br />
| 19 May <br> 24 May <br />
| Final Project Presentations<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12511CDS 140b, Spring 20112011-05-12T04:38:16Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
| <br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12510CDS 140b, Spring 20112011-05-12T04:37:15Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
| <br />
|- valign=top<br />
| 12 May <br> 17 May <br />
| Guest Lectures<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12505CDS 140b, Spring 20112011-05-10T09:58:48Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]<br />
| <br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12495CDS 140b, Spring 20112011-05-05T11:52:46Z<p>Liu: /* Announcements */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 29 Apr 2011: Homework #3 posted; due 12 May 2011<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
| <br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12494CDS 140b, Spring 20112011-05-05T11:51:37Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]<br />
| <br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12493CDS 140b, Spring 20112011-05-05T07:48:19Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
| <br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12489CDS 140b, Spring 20112011-05-03T10:23:52Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko, 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* Regular Perturbation<br />
* Averaging<br />
* Singular Perturbation<br />
* Stability Analysis<br />
|<br />
* Khalil, 10.1-10.2, 10.4, 11.1-10.3, 11.5<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]<br />
| <br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12485CDS 140b, Spring 20112011-05-02T20:03:36Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
* Structural Stability and Peixoto's Theorem<br />
* Various Types of Bifurcations<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <br />
|<br />
* Perko 4.1, 4.2, 4.3<br />
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]<br />
|<br />
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* <br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] <br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12452CDS 140b, Spring 20112011-04-26T04:48:11Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
|<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* <br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Guest_Lecture,_CDS_140B,_Spring_2011&diff=12451Guest Lecture, CDS 140B, Spring 20112011-04-26T04:20:10Z<p>Liu: </p>
<hr />
<div>'''CONTROL OF CYBER-PHYSICAL SYSTEMS: A SYMBOLIC APPROACH'''<br />
<br />
Majid Zamani<br><br />
PhD Candidate<br><br />
University of California at Los Angeles<br><br />
http://www.ee.ucla.edu/~zamani/<br><br />
<br />
Thursday, April 28, 2011<br><br />
10:45 AM to 11:45 AM<br><br />
Steele 214<br><br />
<br />
Cyber-Physical Systems (CPS) are union of two parts: cyber part and physical part. The cyber part includes computational-related objects including both software and hardware. The physical part includes physical objects described by physical laws. The integration of these two parts, termed CPS, forms complex systems providing new capabilities. Although the 20th-century science and technology have provided us with effective methods and tools for analyzing and designing both computational and physical systems, the design and analysis of CPS are not just union of those two fields. Hence, we need a unified framework to design and analyze CPS. Finite state models were proposed by several researchers as a convenient mechanism to design and analyze CPS. In this talk we show how differential equations models for any smooth control systems can be transformed into finite state models.</div>Liuhttps://murray.cds.caltech.edu/index.php?title=Guest_Lecture,_CDS_140B,_Spring_2011&diff=12450Guest Lecture, CDS 140B, Spring 20112011-04-26T04:19:38Z<p>Liu: Created page with 'CONTROL OF CYBER-PHYSICAL SYSTEMS: A SYMBOLIC APPROACH Majid Zamani PhD Candidate University of California at Los Angeles http://www.ee.ucla.edu/~zamani/ Thursday, April 28, 20…'</p>
<hr />
<div>CONTROL OF CYBER-PHYSICAL SYSTEMS: A SYMBOLIC APPROACH<br />
<br />
Majid Zamani<br />
PhD Candidate<br />
University of California at Los Angeles<br />
http://www.ee.ucla.edu/~zamani/<br />
<br />
Thursday, April 28, 2011<br />
10:45 AM to 11:45 AM<br />
Steele 214<br />
<br />
Cyber-Physical Systems (CPS) are union of two parts: cyber part and physical part. The cyber part includes computational-related objects including both software and hardware. The physical part includes physical objects described by physical laws. The integration of these two parts, termed CPS, forms complex systems providing new capabilities. Although the 20th-century science and technology have provided us with effective methods and tools for analyzing and designing both computational and physical systems, the design and analysis of CPS are not just union of those two fields. Hence, we need a unified framework to design and analyze CPS. Finite state models were proposed by several researchers as a convenient mechanism to design and analyze CPS. In this talk we show how differential equations models for any smooth control systems can be transformed into finite state models.</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12449CDS 140b, Spring 20112011-04-26T04:19:18Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]<br />
|<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* <br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12447CDS 140b, Spring 20112011-04-25T03:29:42Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| Guest Lecture<br />
|<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
* <br />
*<br />
*<br />
|<br />
|<br />
|- valign=top<br />
| <br />
|<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12446CDS 140b, Spring 20112011-04-25T03:28:11Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| Guest Lecture<br />
|<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
|<br />
|<br />
|- valign=top<br />
| <br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12445CDS 140b, Spring 20112011-04-25T03:27:49Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| Guest Lecture<br />
|<br />
|<br />
|- valign=top<br />
| 3 May <br> 5 May <br> 10 May<br />
| Averaging and Perturbation<br />
|<br />
|<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12444CDS 140b, Spring 20112011-04-25T03:26:41Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
|<br />
|<br />
|- valign=top<br />
| 28 Apr<br />
| Guest Lecture<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] (Hamed)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems] (Matanya)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12405CDS 140b, Spring 20112011-04-19T01:24:38Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12404CDS 140b, Spring 20112011-04-19T01:24:22Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12403CDS 140b, Spring 20112011-04-19T01:24:11Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
|<br />
[[]]<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12402CDS 140b, Spring 20112011-04-19T01:23:28Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
|<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12401CDS 140b, Spring 20112011-04-19T01:22:46Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
|<br />
<br />
|- valign=top<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12400CDS 140b, Spring 20112011-04-19T01:21:57Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
|- valign=top<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Projects: ==<br />
<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems]<br />
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory]</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12390CDS 140b, Spring 20112011-04-15T08:12:50Z<p>Liu: /* Announcements */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12389CDS 140b, Spring 20112011-04-15T08:12:39Z<p>Liu: /* Announcements */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 14 Apr 2011: Homework #1 is now posted; due 26 Apr 2011<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12388CDS 140b, Spring 20112011-04-15T08:12:02Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
|<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12387CDS 140b, Spring 20112011-04-15T08:11:34Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Bifurcation Theory<br />
*<br />
*<br />
*<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12386CDS 140b, Spring 20112011-04-15T08:10:55Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
| 19 Apr <br> 21 Apr <br> 26 Apr<br />
| Stability Theory<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12385CDS 140b, Spring 20112011-04-15T08:10:13Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
|- valign=top<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12384CDS 140b, Spring 20112011-04-15T08:09:27Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]<br />
|<br />
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12380CDS 140b, Spring 20112011-04-14T04:24:21Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12375CDS 140b, Spring 20112011-04-12T05:44:16Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12351CDS 140b, Spring 20112011-04-07T06:51:32Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12350CDS 140b, Spring 20112011-04-07T06:50:47Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* Recap<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12349CDS 140b, Spring 20112011-04-07T06:49:58Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Stability Theory<br />
* Recap<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/Lecture4.pdf Lecture Note 4]<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12348CDS 140b, Spring 20112011-04-07T06:49:14Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz, 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Lyapunov Stability Theory<br />
* Recap<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil, 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/Lecture4.pdf Lecture Note 4]<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
<br />
=== Policies:===<br />
<br />
'''Lecture notes:''' <br />
<br />
A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
<br />
'''Collaboration Policy''' <br />
<br />
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
<br />
'''Grading Policy''' <br />
<br />
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
<br />
'''Late Homework''' <br />
<br />
Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
<br />
== Old Announcements ==</div>Liuhttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12347CDS 140b, Spring 20112011-04-07T06:48:49Z<p>Liu: /* Lecture Schedule */</p>
<hr />
<div>{| width=100%<br />
|-<br />
| colspan=2 align=center |<br />
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__<br />
|- valign=top<br />
| width=50% |<br />
'''Instructors'''<br />
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)<br />
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)<br />
* Lectures: Tu/Th, 10:30-11:55, 314 ANB<br />
* Office Hours: By appointment<br />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: M 4:30-6:00, 230 ANB<br />
|}<br />
<br />
=== Course Description ===<br />
'''CDS 140b is a continuation of CDS 140a'''. A large part of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.<br />
<br />
===Announcements ===<br />
* 4 Apr 2011: [http://clas.caltech.edu/search/r?SEARCH=cds+140&submit=Submit List of Reserves] (in SFL) for the course has been created<br />
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011<br />
* 18 Mar 2011: web page creation<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading/Lecture Notes'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar <br> 5 Apr<br />
| Limit cycles<br />
* Recap<br />
* Ruling out closed orbits<br />
* Index theory<br />
* Poincare-Bendixon theorem<br />
* Lienard systems<br />
| <br />
* Strogatz 7.0-7.4 <br><br />
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br><br />
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]<br />
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]<br />
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]<br />
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]<br />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 7 Apr <br> 12 Apr <br> 14 Apr<br />
| Lyapunov Stability Theory<br />
* Recap<br />
* LaSalle's invariance principle<br />
* Stability of nonautonomous systems<br />
* Linearization and converse theorems<br />
* Boundedness and input-to-state stability<br />
* Stability of perturbed systems<br />
| <br />
* Khalil 4.1-4.9, 9.1-9.2 <br><br />
* [http://www.cds.caltech.edu/~liu/Lecture4.pdf Lecture Note 4]<br />
<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
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'''Additional Sources:'''<br />
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* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777<br />
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=== Policies:===<br />
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'''Lecture notes:''' <br />
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A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted. <br />
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'''Collaboration Policy''' <br />
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Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed. <br />
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'''Grading Policy''' <br />
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The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). <br />
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'''Late Homework''' <br />
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Each student is allowed one ''late day'' which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.<br />
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== Old Announcements ==</div>Liu