Three-Dimensional Autonomous Systems and Chaos

Aims and Objectives

• To introduce first-order ODEs in three variables.

• To plot phase portraits and chaotic attractors.

• To identify chaos.

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

• construct phase portraits for linear systems in three dimensions;

• use the Maple package to plot phase portraits and time series for nonlinear systems;

• identify chaotic solutions;

• interpret the solutions to modeling problems taken from various scientific disciplines, and, in particular, chemical kinetics, electric circuits, and meteorology.