https://murray.cds.caltech.edu/api.php?action=feedcontributions&user=Motee&feedformat=atomMurray Wiki - User contributions [en]2021-12-02T01:07:34ZUser contributionsMediaWiki 1.35.3https://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12472CDS 140b, Spring 20112011-04-30T00:23:46Z<p>Motee: /* 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 />
|<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12471CDS 140b, Spring 20112011-04-30T00:23:24Z<p>Motee: /* 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 />
[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 />
|<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12470CDS 140b, Spring 20112011-04-30T00:22:25Z<p>Motee: /* 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 />
|<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12469CDS 140b, Spring 20112011-04-30T00:21:26Z<p>Motee: /* 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 />
| [http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]<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/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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12464CDS 140b, Spring 20112011-04-27T23:43:35Z<p>Motee: /* Projects: */</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 />
* 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 />
|- 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/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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12463CDS 140b, Spring 20112011-04-27T20:56:48Z<p>Motee: /* Projects: */</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 />
* 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 />
|- 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/contraction.pdf Contraction Analysis]<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]<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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12462CDS 140b, Spring 20112011-04-27T20:50:23Z<p>Motee: /* Projects: */</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 />
* 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 />
|- 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/contraction.pdf Contraction Analysis]<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]<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12461CDS 140b, Spring 20112011-04-27T20:47:06Z<p>Motee: /* Projects: */</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 />
* 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 />
|- 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/contraction.pdf Contraction Analysis]<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/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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12460CDS 140b, Spring 20112011-04-27T20:46:40Z<p>Motee: /* Projects: */</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 />
* 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 />
|- 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/contraction.pdf Contraction Analysis<br />
for Nonlinear Systems]<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/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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12459CDS 140b, Spring 20112011-04-27T18:58:59Z<p>Motee: /* 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 />
* 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 />
|- 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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12458CDS 140b, Spring 20112011-04-27T18:58:07Z<p>Motee: /* 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/~motee/HW2.pdf Homework 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/~liu/CDS140b/lecture7-9.pdf Lecture Notes 7, 8, and 9]<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12457CDS 140b, Spring 20112011-04-27T18:57:29Z<p>Motee: /* 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 />
* 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/~liu/CDS140b/lecture7-9.pdf Lecture Notes 7, 8, and 9]<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12456CDS 140b, Spring 20112011-04-27T18:55:30Z<p>Motee: /* 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 />
* 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 />
|<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12455CDS 140b, Spring 20112011-04-27T18:52:37Z<p>Motee: /* 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 />
* Structural Stability<br />
* Various Types of Bifurcations: Saddle-Node, Transcritical, Pitchfork<br />
* Higher-Dimensional Bifurcation<br />
* Unfoldings of Bifurcations <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12448CDS 140b, Spring 20112011-04-25T20:36:57Z<p>Motee: /* Projects: */</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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12428CDS 140b, Spring 20112011-04-20T23:54:14Z<p>Motee: /* Projects: */</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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12427CDS 140b, Spring 20112011-04-20T22:24:51Z<p>Motee: /* Projects: */</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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12422CDS 140b, Spring 20112011-04-20T02:40:46Z<p>Motee: /* Projects: */</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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12421CDS 140b, Spring 20112011-04-20T02:33:29Z<p>Motee: /* Projects: */</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] (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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12420CDS 140b, Spring 20112011-04-20T02:32:10Z<p>Motee: /* Projects: */</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] (Matanya)<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12419CDS 140b, Spring 20112011-04-20T02:31:20Z<p>Motee: /* Projects: */</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](Matanya)<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12399CDS 140b, Spring 20112011-04-18T22:04:47Z<p>Motee: /* Projects: */</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 />
== 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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12398CDS 140b, Spring 20112011-04-18T22:04:13Z<p>Motee: /* Old 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 />
== 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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12340CDS 140b, Spring 20112011-04-06T00:01:38Z<p>Motee: </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 />
*<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12339CDS 140b, Spring 20112011-04-06T00:00:11Z<p>Motee: /* 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 />
| 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 />
*<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12337CDS 140b, Spring 20112011-04-05T05:43:45Z<p>Motee: /* 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 />
| 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 />
<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 />
*<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12318CDS 140b, Spring 20112011-04-03T06:09:55Z<p>Motee: /* 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 />
| 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 />
* 18 Mar 2011: web page creation<br />
<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 />
<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 />
*<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 />
* 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 />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12317CDS 140b, Spring 20112011-04-03T06:07:23Z<p>Motee: /* 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 />
| 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 />
* 18 Mar 2011: web page creation<br />
<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 />
| 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 />
<br />
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]<br />
<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<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 />
* 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 />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12303CDS 140b, Spring 20112011-03-31T08:32:37Z<p>Motee: /* 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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]<br />
* Office hours: TBA<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 />
* 18 Mar 2011: web page creation<br />
<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 />
| 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 />
<br />
| [[CDS 140b Spring 2011 Homework 1|Home Work 1]]<br />
<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<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 />
* 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 />
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893<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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12282CDS 140b, Spring 20112011-03-29T16:46:22Z<p>Motee: </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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* Jerry Cruz<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
| '''Lecture Note'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
| [[CDS 140b Spring 2011 Lecture Note 1|Lecture Note 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<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 />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 and final projects. <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12281CDS 140b, Spring 20112011-03-29T16:21:27Z<p>Motee: /* 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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
| '''Lecture Note'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
| [[CDS 140b Spring 2011 Lecture Note 1|Lecture Note 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<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 />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 and final projects. <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b_Spring_2011_Lecture_Note_1&diff=12280CDS 140b Spring 2011 Lecture Note 12011-03-29T16:19:54Z<p>Motee: </p>
<hr />
<div>[http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b_Spring_2011_Lecture_Note_1&diff=12279CDS 140b Spring 2011 Lecture Note 12011-03-29T16:18:30Z<p>Motee: </p>
<hr />
<div>[http://www.cds.caltech.edu/~motee/lecture1.pdf Lecture Note 1]</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b_Spring_2011_Lecture_Note_1&diff=12278CDS 140b Spring 2011 Lecture Note 12011-03-29T16:18:06Z<p>Motee: Created page with '[http://www.cds.caltech.edu/~motee/lecture1.pdf link title]'</p>
<hr />
<div>[http://www.cds.caltech.edu/~motee/lecture1.pdf link title]</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12266CDS 140b, Spring 20112011-03-23T19:23:14Z<p>Motee: /* References: */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<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 />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 and final projects. <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12265CDS 140b, Spring 20112011-03-23T19:21:28Z<p>Motee: /* Policies: */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 and final projects. <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12264CDS 140b, Spring 20112011-03-23T19:21:01Z<p>Motee: /* Policies: */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 determined based on homework sets and final projects. <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>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12263CDS 140b, Spring 20112011-03-23T19:20:23Z<p>Motee: </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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 grade will be determined based on homework sets and final projects. <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 />
<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12262CDS 140b, Spring 20112011-03-23T19:19:27Z<p>Motee: </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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 />
<br />
'''Grading Policy''' <br />
<br />
The grade will be determined based on homework sets and final projects. <br />
<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 />
<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12261CDS 140b, Spring 20112011-03-23T19:12:58Z<p>Motee: </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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 at least an hour before each lecture (typically the night before) 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 />
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 />
<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12260CDS 140b, Spring 20112011-03-23T19:12:27Z<p>Motee: </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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<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 at least an hour before each lecture (typically the night before) 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 />
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 />
<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12259CDS 140b, Spring 20112011-03-23T19:00:45Z<p>Motee: /* References */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References: ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777.<br />
<br />
=== Grading ===<br />
<br />
<br />
=== Collaboration Policy ===<br />
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructors. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12258CDS 140b, Spring 20112011-03-23T19:00:32Z<p>Motee: /* Textbooks */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== References ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777.<br />
<br />
=== Grading ===<br />
<br />
<br />
=== Collaboration Policy ===<br />
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructors. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12257CDS 140b, Spring 20112011-03-23T18:59:47Z<p>Motee: /* Textbooks */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== Textbooks ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,Springer, 2ed Edition, 1996.<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777.<br />
<br />
=== Grading ===<br />
<br />
<br />
=== Collaboration Policy ===<br />
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructors. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12256CDS 140b, Spring 20112011-03-23T18:59:23Z<p>Motee: /* Textbooks */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== Textbooks ===<br />
<br />
'''Course Textbooks'''<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional Sources:'''<br />
<br />
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,<br />
Springer, 2ed Edition, 1996.<br />
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777.<br />
<br />
=== Grading ===<br />
<br />
<br />
=== Collaboration Policy ===<br />
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructors. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2011&diff=12255CDS 140b, Spring 20112011-03-23T18:53:47Z<p>Motee: /* Textbooks */</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 />
| width=50% |<br />
'''Teaching Assistant'''<br />
* TBA<br />
* Office hours: TBA<br />
|}<br />
<br />
=== Course Description ===<br />
<br />
<br />
===Announcements ===<br />
* 18 Mar 2011: web page creation<br />
<br />
<br />
=== Lecture Schedule ===<br />
<br />
{| width=100% border=1 cellspacing=0 cellpadding=5<br />
|-<br />
| '''Date'''<br />
| '''Topic'''<br />
| '''Reading'''<br />
| '''Homework'''<br />
|- valign=top<br />
|- valign=top<br />
| 29 Mar <br> 31 Mar<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 />
Notes:<br />
*<br />
*<br />
| [[CDS 140b Spring 2011 Homework 1|HW 1]]<br />
|- valign=top<br />
| 5 Apr <br> 7 Apr<br />
| Bifurcation<br />
* <br />
*<br />
*<br />
*<br />
*<br />
<br />
| <!-- Reading --><br />
| <!-- Homework --><br />
|}<br />
<br />
=== Textbooks ===<br />
<br />
The suggested textbooks for the course (available via the online bookstore) are<br />
<br />
* Strogatz, Steven; Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536<br />
* Perko, Lawrence; Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164<br />
<br />
'''Additional sources:'''<br />
<br />
=== Grading ===<br />
<br />
<br />
=== Collaboration Policy ===<br />
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructors. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.<br />
<br />
== Old Announcements ==</div>Moteehttps://murray.cds.caltech.edu/index.php?title=Pablo_Parrilo,_Nov_2010&diff=11549Pablo Parrilo, Nov 20102010-11-19T19:59:54Z<p>Motee: /* Agenda */</p>
<hr />
<div>Pablo Parrilo will be visiting Caltech on 23 Nov 2010 (Tue). Sign up for a time to meet with him below.<br />
<br />
=== Agenda ===<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Richard Murray (109 Steele)}}<br />
{{agenda item|11:00a|Seminar: 214 Steele}}<br />
{{agenda item|12:00p|Lunch with John, (faculty: add your name to the list if you want to come)}}<br />
{{agenda item|1:30p|Nader (Annenberg) }}<br />
{{agenda item|2:15|John Doyle (Annenberg)}}<br />
{{agenda item|2:30p|CDS 212 (Annenberg)}}<br />
{{agenda item|4:00p|Genti (Annenberg)}}<br />
{{agenda item|4:45p|Open}}<br />
{{agenda end}}<br />
<br />
=== Seminar ===<br />
<br />
'''FLOWS AND DECOMPOSITIONS OF GAMES: HARMONIC AND POTENTIAL GAMES'''<br />
<br />
Pablo A. Parrilo (Massachusetts Institute of Technology)<br />
<br />
Tuesday, November 23, 2010<br><br />
11:00 AM to 12:00 PM<br><br />
Steele 214<br />
<br />
Exact potential games are those where the preferences of the strategy<br />
profiles of the different players are globally consistent, and therefore<br />
the players' payoffs can be aggregated through a joint function. In this<br />
talk, we analyze the general situation where there are local or global<br />
inconsistencies between the preferences of the different players. For<br />
this, we introduce a natural decomposition of multiplayer games in terms<br />
of potential and harmonic components. Besides its intrinsic interest,<br />
this decomposition facilitates the study of equilibrium and convergence<br />
properties of natural game dynamics. We discuss the implications for<br />
cooperative control problems, pricing schemes, and efficiency loss, and<br />
illustrate the results and techniques through an example of power<br />
control in wireless networks. Joint work with Ozan Candogan, Ishai<br />
Menache, and Asu Ozdaglar (MIT), http://arxiv.org/abs/1005.2405</div>Moteehttps://murray.cds.caltech.edu/index.php?title=Pablo_Parrilo,_Nov_2010&diff=11548Pablo Parrilo, Nov 20102010-11-19T19:59:29Z<p>Motee: /* Agenda */</p>
<hr />
<div>Pablo Parrilo will be visiting Caltech on 23 Nov 2010 (Tue). Sign up for a time to meet with him below.<br />
<br />
=== Agenda ===<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Richard Murray (109 Steele)}}<br />
{{agenda item|11:00a|Seminar: 214 Steele}}<br />
{{agenda item|12:00p|Lunch with John, (faculty: add your name to the list if you want to come)}}<br />
{{agenda item|1:30p|Nader}}<br />
{{agenda item|2:15|John Doyle (Annenberg)}}<br />
{{agenda item|2:30p|CDS 212 (Annenberg)}}<br />
{{agenda item|4:00p|Genti (Annenberg)}}<br />
{{agenda item|4:45p|Open}}<br />
{{agenda end}}<br />
<br />
=== Seminar ===<br />
<br />
'''FLOWS AND DECOMPOSITIONS OF GAMES: HARMONIC AND POTENTIAL GAMES'''<br />
<br />
Pablo A. Parrilo (Massachusetts Institute of Technology)<br />
<br />
Tuesday, November 23, 2010<br><br />
11:00 AM to 12:00 PM<br><br />
Steele 214<br />
<br />
Exact potential games are those where the preferences of the strategy<br />
profiles of the different players are globally consistent, and therefore<br />
the players' payoffs can be aggregated through a joint function. In this<br />
talk, we analyze the general situation where there are local or global<br />
inconsistencies between the preferences of the different players. For<br />
this, we introduce a natural decomposition of multiplayer games in terms<br />
of potential and harmonic components. Besides its intrinsic interest,<br />
this decomposition facilitates the study of equilibrium and convergence<br />
properties of natural game dynamics. We discuss the implications for<br />
cooperative control problems, pricing schemes, and efficiency loss, and<br />
illustrate the results and techniques through an example of power<br />
control in wireless networks. Joint work with Ozan Candogan, Ishai<br />
Menache, and Asu Ozdaglar (MIT), http://arxiv.org/abs/1005.2405</div>Moteehttps://murray.cds.caltech.edu/index.php?title=Raff_D%27Andrea,_12_October_2010&diff=11352Raff D'Andrea, 12 October 20102010-10-03T21:05:38Z<p>Motee: /* Schedule */</p>
<hr />
<div>Raff D'Andrea from ETH will be visiting Caltech on 12 October 2010 (Tue). Please sign up for a time to meet with him below.<br />
<br />
=== Schedule ===<br />
<br />
Tuesday (12 Oct 2010):<br />
<blockquote><br />
{{agenda begin}}<br />
{{agenda item|8:45a|Open}}<br />
{{agenda item|9:30a|Open}}<br />
{{agenda item|10:15a|Open}}<br />
{{agenda item|11:00a|Open}}<br />
{{agenda item|12:00p|IST Lunch Bunch, Annenberg}}<br />
{{agenda item|1:30p|Open}}<br />
{{agenda item|2:15p| Nader}}<br />
{{agenda item|3:00p|Meeting with RMM students}}<br />
{{agenda item|4:15p|Open}}<br />
{{agenda end}}<br />
</blockquote><br />
<br />
=== Talk Abstract ===<br />
<br />
'''Some Applications of Distributed Estimation and Control'''<br />
<br />
Raff D'Andrea, ETHZ<br />
<br />
In this talk I will discuss several applications of<br />
distributed estimation and control: Kiva Systems, a company<br />
that uses hundreds of mobile robots to move inventory in<br />
distribution facilities; the Balancing Cube, a structure that can <br />
balance on any one of its edges or corners using six rotating <br />
mechanisms on the cube's inner faces; the Distributed Flight Array, <br />
a flying platform consisting of multiple autonomous single propeller vehicles<br />
that are able to drive, dock with their peers, and fly in a coordinated fashion; <br />
the Flying Machine Arena, a research-driven airspace where vehicles teach <br />
themselves -- and each other -- how to fly.<br />
<br />
Raffaello D'Andrea is Professor of Dynamic Systems and Control<br />
at ETH Zurich and Technical Co-Founder of Kiva Systems, a<br />
company that develops adaptive and self-configuring warehouse<br />
automation systems using hundreds of networked, mobile robots.<br />
Also a creator of dynamic sculpture, he has shown his work at<br />
international venues including the Venice Biennale, the<br />
Luminato Festival, Ars Electronica, and ideaCity; two of his<br />
pieces are in the permanent collection of the National Gallery<br />
of Canada.</div>Moteehttps://murray.cds.caltech.edu/index.php?title=Jan_2010_meetings&diff=10192Jan 2010 meetings2010-01-07T20:18:36Z<p>Motee: /* 14 Jan (Thu) */</p>
<hr />
<div>The list below has times that I am available to meet on 12-14 Jan. <br />
* One-on-one meetings: Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and see if you can switch). <br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=30%><br />
==== 12 Jan (Tue) ====<br />
{{agenda begin}}<br />
{{agenda item|4:00p|Open - 60m}}<br />
{{agenda item|5:00p|Dom - 30m}}<br />
{{agenda item|5:30p|Shuo - 60m}}<br />
{{agenda item|6:30p|Andrea - 60m}}<br />
{{agenda end}}<br />
<br />
</td><td width=30%><br />
<br />
==== 13 Jan (Wed) ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Dionysios - 45m}}<br />
{{agenda item|10:15a| Mumu - 45m}}<br />
{{agenda item|11:00a| Vanessa - 60m}}<br />
{{agenda item||}}<br />
{{agenda item|1:30p|Open - 30m}}<br />
{{agenda item|2:00p|Exam}}<br />
{{agenda item|3:30p|Open - 60m}}<br />
{{agenda item|4:30p|cisco - 60m}}<br />
{{agenda item|5:30p|Ufuk - 60m}}<br />
{{agenda end}}<br />
</td><td width=30%><br />
<br />
==== 14 Jan (Thu) ====<br />
{{agenda begin}}<br />
{{agenda item|9:00a|Exam}}<br />
{{agenda item|10:30a|Nok - 45m}}<br />
{{agenda item|11:15a|Javad & Somayeh - 45m}}<br />
{{agenda item||}}<br />
{{agenda item|1:30p|Nader - 30m}}<br />
{{agenda item|2:00p|Pete - 60m}}<br />
{{agenda item|3:00p|Ophelia - 60m}}<br />
{{agenda item|4:00p|Open - 30m}}<br />
{{agenda item|4:30p|Exam}}<br />
{{agenda item|6:30p|Open - 60m}}<br />
{{agenda end}}<br />
</td></tr><br />
</table></div>Motee