Three-Dimensional Autonomous Systems and Chaos

Stephen Lynch ()
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Stephen Lynch: Manchester Metropolitan University, Department of Computing and Mathematics

Chapter 7 in Dynamical Systems with Applications using Maple¿, 2010, pp 147-171 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4605-9_8

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