Mathematics 532H - NonlinearDyn&ChaosW/Applicatns

This course provides an introduction to systems of differential equations and dynamical systems, as well as chaotic dynamics, while providing a significant set of connections with phenomena modeled through these approaches in Physics, Chemistry, and Biology. From the mathematical perspective, geometric and analytical methods of describing the behavior of solutions will be developed and illustrated in the context of low-dimensional systems, including behavior near fixed points and periodic orbits, phase portraits, Lyapunov stability, Hamiltonian systems, bifurcation phenomena, and chaotic dynamics. From the applied perspective, numerous specific applications will be touched upon ranging from the laser to the synchronization of fireflies, and from the outbreaks of insects to chemical reactions or even prototypical models of love affairs. In addition to the theoretical component, a self-contained computational component towards addressing these systems will be developed with the assistance of MATLAB (and wherever relevant Mathematica). However, no prior knowledge of these packages will be assumed.