View source for CDS 140b, Spring 2011

{| width=100%
|-
| colspan=2 align=center |
<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* [http://www.cds.caltech.edu/people/853 Nader Motee] (CDS)
* [http://www.cds.caltech.edu/people/974 Jun Liu] (CDS)
* Lectures: Tu/Th, 10:30-11:55, 314 ANB
* Office Hours: By appointment
| width=50% |
'''Teaching Assistant'''
* [http://www.cds.caltech.edu/people/671 Jerry Cruz]
* Office hours: M 4:30-6:00, 230 ANB
|}

=== Course Description ===
'''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.

===Announcements ===
* 11 May 2011: Homework #4 posted; due 31 May 2011
* 29 Apr 2011: Homework #3 posted; due 12 May 2011
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011
* 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
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011
* 18 Mar 2011: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Date'''
| '''Topic'''
| '''Reading/Lecture Notes'''
| '''Homework'''
|- valign=top
|- valign=top
| 29 Mar <br> 31 Mar <br> 5 Apr
| Limit cycles
* Recap
* Ruling out closed orbits
* Index theory
* Poincare-Bendixon theorem
* Lienard systems
| 
* Strogatz, 7.0-7.4 <br>
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br>
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]

| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]
[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]

|- valign=top
| 7 Apr <br>  12 Apr <br> 14 Apr
| Stability Theory
* LaSalle's invariance principle
* Stability of nonautonomous systems
* Linearization and converse theorems
* Boundedness and input-to-state stability
* Stability of perturbed systems
| 
* Khalil, 4.1-4.9, 9.1-9.2 <br>
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]
|
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]

[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]
|- valign=top
| 19 Apr <br>  21 Apr <br> 26 Apr
| Bifurcation Theory
* Structural Stability and Peixoto's Theorem
* Various Types of Bifurcations
* Higher-Dimensional Bifurcation
* Unfoldings of Bifurcations 
|
* Perko, 4.1, 4.2, 4.3
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]
|
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]

[http://www.cds.caltech.edu/~jerry/scan0001.pdf Solutions 3]
|- valign=top
| 28 Apr
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]
|
|- valign=top
| 3 May <br>  5 May <br> 10 May
| Averaging and Perturbation
* Regular Perturbation
* Periodically Perturbed Systems
* Averaging
* Singular Perturbation
* Stability Analysis
|
* Khalil, 10.1-10.4, 11.1-10.3, 11.5
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]
* [http://www.cds.caltech.edu/~liu/CDS140b/Perturbation.pdf Notes on Perturbation]
| [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]
|- valign=top
| 12 May <br> 17 May 
| Guest Lectures
| <!-- Reading -->
| <!-- Homework -->
|- valign=top
| 19 May <br> 24 May 
| Final Project Presentations
| <!-- Reading -->
| <!-- Homework -->
|}

=== References: ===

'''Course Textbooks'''

* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164

'''Additional Sources:'''

* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777

=== Policies:===

'''Lecture notes:''' 

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. 

'''Collaboration Policy''' 

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. 

'''Grading Policy''' 

The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%). 

'''Late Homework''' 
 
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.

== Projects: ==

* [http://www.cds.caltech.edu/~motee/CDS140b/Bifurcation-Control.pdf Bifurcation Control]
* [http://www.cds.caltech.edu/~motee/CDS140b/contraction.pdf Contraction Analysis] (Lingwen)
* [http://www.cds.caltech.edu/~motee/CDS140b/Emergent-Behavior-in-Flocks.pdf Emergent Behavior in Flocks] 
* [http://www.cds.caltech.edu/~motee/CDS140b/mathematics-of-emergence.pdf Mathematics of Emergence] (Hamed)
* [http://www.cds.caltech.edu/~motee/CDS140b/oscillations-monotone.pdf Oscillations in I/O Monotone Systems] 
* [http://www.cds.caltech.edu/~motee/CDS140b/BIOLOGICAL-OSCILLATORS.pdf Biological Oscillators and Synchronization] (Marcella)
* [http://www.cds.caltech.edu/~motee/CDS140b/Model-Reduction.pdf Model Reduction in Biological Systems] 
* [http://www.cds.caltech.edu/~motee/CDS140b/MultiStability-Monotone.pdf MultiStability and Monotone Systems] (Enoch)
* [http://www.cds.caltech.edu/~motee/CDS140b/stability_switching.pdf Stability of Switching Systems]  (Matanya)
* [http://www.cds.caltech.edu/~motee/CDS140b/string_stability.pdf String Stability of Interconnected Systems] (Eric)
* [http://www.cds.caltech.edu/~motee/CDS140b/Synchronization-Contraction.pdf Synchronization Using Contraction Theory] (Tom)