This unit is an introduction to the modern theory of dynamical systems which includes applications and a discussion of chaos. Chaos has shown itself to be an apt description of many phenomena of physics, biology and medicine. The basic properties of ordinary differential equations are examined—existence and uniqueness of trajectories, continuation, invariant sets, equilibria, linearisation and stability, Lyapunov functions, Poincare-Bendixson theorem, degree theory and local bifurcations. The connection between maps and flows is established through local sections and the properties of maps developed—fixed points, stability, bifurcations of one-dimensional maps, horseshoe maps and chaos.... -- Course Website
Instructor: Professor Kevin Judd
Prerequisites: MATH2209 Calculus and Probability and MATH2020 Multivariable Calculus and Linear Algebra
