Students in Math, Sciences and Engineering interested in modelling and Chaos
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.
- 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.