415 - Applied Dynamical Systems, Chaos and Modeling
Prerequisites:
Math 319 or 320, or consent of instructor.
Frequency:
Fall (I)
Student Body:
Students in Math, Sciences and Engineering interested in modelling and Chaos
Credits:
3. (N-A) Recent Texts:
Strogatz, S. H. Nonlinear Dynamics and Chaos.
Course Coordinator:
Amir Assadi Background and Goals:
An introduction to nonlinear dynamical systems including stability, bifurcations and chaos. The course will give underlying mathematical ideas, but emphasize applications from many scientific fields.
Alternatives:
N/A
Subsequent Courses:
N/A Course Content:
- One-dimensional maps and difference equations: linear and nonlinear problems, graphical solutions, bifurcations, chaos.
- First-order differential equations (one-dimensional flows): linear and nonlinear equations, graphical solutions, bifurcations.
- Two-dimensional flows: phase plane, stability of fixed points, periodic solutions, and limit cycles. Introduction to bifurcation theory, local and global bifurcations. Tools for studying global behavior of flows: Lyapunov functions, Poincare-Bendixson Theorem, gradient flows.
- Three-dimensional flows: Lyapunov exponents, Poincare sections, strange attractors, chaos.