Nonlinear Discrete Dynamical Systems

Aims and Objectives

• To introduce nonlinear one- and two-dimensional iterated maps.

• To investigate period-doubling bifurcations to chaos.

• To introduce the notion of universality.

On completion of this chapter, the reader should be able to

• produce graphical iterations of one-dimensional iterated maps;

• test whether certain systems are chaotic;

• plot bifurcation diagrams;

• apply some of the theory to model simple problems from biology, economics, neural networks, nonlinear optics, and population dynamics.