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.
KeywordsLyapunov Exponent Rayleigh Number Phase Portrait Unstable Manifold Chaotic Attractor
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