CDS 240, Spring 2016
Nonlinear Dynamical Systems
CDS 240. Nonlinear Dynamical Systems. 9 units (3-0-6); 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.
|Week||Date||Topic||Suggested Reading/Lecture Notes||Homework|
|Stability of perturbed systems
||HW #1 |
Due 11 Apr
||HW #2 |
Due 25 Apr
|Lagrangian and Hamiltonian systems
||HW #3 |
Due 9 May
|6||4 May |
|Nonnormal systems||See dropbox folder||HW #4 |
Due 25 May
|8||13 May |
- H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
- S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
- F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346
- L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164
- S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777
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.
The final grades will be evaluated based on homework assignments.