Authorised by Academic Registrar, April 1996
Objectives On the completion of this subject students will be able to appreciate and understand chaotic discrete systems using elementary mathematical concepts; study the dynamics of one dimensional discrete systems and determine conditions under which they reach a steady state, oscillate or eventually become chaotic; analyse in some detail the logistic equation and similar systems and examine the phenomena of period doubling and universality; apply the mathematics to physical and biological contexts, including population modelling; understand how dynamical systems produce fractals, in particular Mandelbrot and Julia sets.
Synopsis Theory, modelling and evolution of discrete dynamical systems. Deterministic and chaotic systems: investigations and applications to physical, biological and ecological systems. The logistic equation, fractals, Julia sets and Mandelbrot sets. Two- dimensional maps. Use of the computer algebra package DERIVE.
Assessment Examinations (2 hours): 85% + Assignment: 7% + Tests (4): 8%