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Three-Dimensional Autonomous Systems and Chaos

  • Stephen Lynch
Chapter

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.

Keywords

Lyapunov Exponent Rayleigh Number Phase Portrait Unstable Manifold Chaotic Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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