Applied Dynamical Systems

AMS 114/214 Introduction to Dynamical Systems 

Instructor: Qi Gong, Associate Professor, BE 361A, email: qigong@soe.ucsc.edu

Lecture: TuTH 8:00AM - 9:45AM, Kresge Clrm 319

Textbook: Nonlinear Dynamics and Chaos by Steven H. Strogatz, 1st edition, Westview Press 

Suggested supplemental reading: 

  • An Introduction to Chaotic Dynamical Systems by Robert Devaney, 2nd Edition, Westview Press
  • Nonlinear Systems by Hassan K. Khalil, 3rd Edition, Prentice Hall

Office Hours

  • Wednesday, 1:00PM - 2:30PM, BE 361A

Homework: Homework will be due weekly on Tuesday at the beginning of class. AMS 114 and 214 students will have different sets of homework problems. Late homework is NEVER accepted. Please print your name and Student ID clearly on the first page of your homework.

Exams: There will be one mid-term exam around week 5 or 6, and a final exam on Tuesday, March 17, 8:00AM - 11:00AM. Students have the option to work on a final project instead of taking the final exam. 

Grading: Homework: 30%,   Midterm: 30%,   Final 40%

Tentative Schedule (will be updated) 

  • Week 1. Introduction to dynamical systems, how to use ode45 in MATLAB to numerically solve differential equaitons, fixed points and stability, linear stability analysis. Read Chapter 1, Section 2.0, 2.1, 2.2, 2.4 and 2.8.
  • Week 2. Existence and uniqueness of solutions to ODE, impossibility of oscillations in 1D continuous systems, Saddle-Node, Transcritical, and Pitchfork bifurcations. Read Section 2.3, 2.5, 2.6, 3.0, 3.1, 3.2, ans 3.4.
  • Week 3. Imperfect bifurcations (Section 3.6, Section 3.7), and linear systems (Chapter 5).
  • Week 4. Lyapunov Stability Theory. 
  • Week 5. Phase plane (Section 6.1, 6.2 and 6.3), conservative systems (Section 6.5), reversible systems (Section 6.6), and index theory (Section 6.8)
  • Week 6. Introduction to limit cycles (Section 7.0 - 7.2), and Midterm exam
  • Week 7. Ruling out closed orbit (Section 7.2), Poincare Bendixson Theorem (Section 7.3), and Lienard systems (Section 7.4).
  • Week 8. Bifurcations in two dimensional systems (Section 8.0 - 8.3).
  • Week 9. Chaos - Lorenz system (Chapter 9).
  • Week 10 One-dimension maps (Chapter 10).

 

Academic Honesty: See explanation at http://www.ucsc.edu/academics/academic_integrity/index.html

 

Students with disabilities: If you qualify for classroom accommodations because of a disability, please get an Accommodation Authorization from the Disability Resource Center (DRC) and submit it to me in person outside of class (e.g., office hours) within the first two weeks of the quarter. Contact DRC at 459-2089 (voice), 459-4806 (TTY), or http://drc.ucsc.edu for more information on the requirements and/or process.

Instructors and Assistants