35438 Nonlinear Dynamical Systems

Requisite(s): 35231 Differential Equations AND 35321 Analysis 1

These requisites may not apply to students in certain courses. See access conditions.

This subject aims to introduce basic ideas in the qualitative theory of solutions of ordinary differential equations. The features of both two-dimensional and higher dimensional systems are considered. The theory is developed to the stage where basic ideas about limit cycles, strange attractors, chaos and bifurcations can be presented.

Topics in this subject include: review of linear systems; nonlinear systems; phase plane analysis; linearisation; local stability and instability; global asymptotic stability; stable and unstable manifolds; limit cycles and strange attractors; introduction to chaos theory; asymptotic methods; the methods of Poincaré and Lindstedt; the method of averaging; and applications to the theory of finance.

Typical availability

Autumn semester, City campus