CDS 140b, Spring 2012

From MacMynowski
(Difference between revisions)
Jump to: navigation, search
Line 116: Line 116:
 
| <!-- Homework -->
 
| <!-- Homework -->
 
|}
 
|}
 +
<!-- Lecture schedule from previous year
 +
{| 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: ===
 
=== References: ===

Revision as of 16:17, 21 March 2012

This will be the homepage for CDS 140b for Winter 2012.

Introduction to Dynamics

Instructors

Teaching Assistant

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

  • 17 Mar 2012: At least one student has a conflict with the class time; we will see if we can find a time compatible with everyone during the first week of the quarter.
  • 17 Mar 2012: Doug MacMynowski is traveling the first few weeks of the quarter; direct all questions to Shaunak...
  • 17 Mar 2012: web page creation: the list of topics below has not yet been edited from last year; please ignore!

Lecture Schedule

Date Topic Reading/Lecture Notes Homework
29 Mar
31 Mar
5 Apr
Limit cycles
  • Recap
  • Ruling out closed orbits
  • Index theory
  • Poincare-Bendixon theorem
  • Lienard systems
Homework 1

Solutions 1

7 Apr
12 Apr
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

Homework 2

Solutions 2

19 Apr
21 Apr
26 Apr
Bifurcation Theory
  • Structural Stability and Peixoto's Theorem
  • Various Types of Bifurcations
  • Higher-Dimensional Bifurcation
  • Unfoldings of Bifurcations

Homework 3

Solutions 3

28 Apr Guest Lecture Lecture Slides
3 May
5 May
10 May
Averaging and Perturbation
  • Regular Perturbation
  • Periodically Perturbed Systems
  • Averaging
  • Singular Perturbation
  • Stability Analysis
Homework 4
12 May
17 May
Guest Lectures
19 May
24 May
Final Project Presentations

| |

References:

Course Textbooks

  • H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
  • 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:

  • 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:

Personal tools
External