CDS 240, Spring 2016
Nonlinear Dynamical Systems  
Instructors

Teaching Assistant

Course Description
CDS 240. Nonlinear Dynamical Systems. 9 units (306); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Doyle, Murray.
Lecture Schedule
Week  Date  Topic  Suggested Reading/Lecture Notes  Homework 
1  28 Mar 30 Mar RMM 
Stability of perturbed systems

HW #1 Due 11 Apr  
3  1 Apr 6 Apr RMM 
Perturbation theory


3  11 Apr 13 Apr 15 Apr JCD 
Interconnected Systems

HW #2 Due 25 Apr  
4  18 Apr 20 Apr 22 Apr JCD 25 Apr 

5  27 Apr 29 Apr RMM 
Lagrangian and Hamiltonian systems

HW #3 Due 9 May  
6  4 May 6 May RMM  
7  9 May 11 May JCD 
Nonnormal systems  See dropbox folder  HW #4 Due 25 May 
8  13 May 16 May JCD  
9  23 May 25 May RMM 
TBD 
References:
Course Textbooks
 H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 9780130673893
 S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 9780738204536
 F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 9783540609346
Additional Sources:
 L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 9780387951164
 S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 9780387001777
Policies
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.