Math 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: Paul Milewski
• 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

Content coverage:

• 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.