electiveHQ

This module provides an introduction to the theory of dynamical systems leading up to the concept of chaos. The course starts by considering one-dimensional flow, identifying fixed points, classifying stability, and introducing the saddle-node, transcritical and pitchfork bifurcations. We then progress to two-dimensional flows, and discuss classification of linear systems, methods of plotting the phase plane, and limit cycles. We will consider the behaviour of conservative systems, reversible systems and Liénard systems and discuss the Poincaré-Bedixson theorem and Hopf bifurcations. Finally, we will look at chaotic systems, and study one-dimensional maps, fractals and strange attractors.