Exploring Chaos: Theory and Experiment

Exploring Chaos: Theory and Experiment

by Brian Davies, Brian Davies
     
 

ISBN-10: 0738200905

ISBN-13: 9780738200903

Pub. Date: 08/04/1999

Publisher: Westview Press

This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and

Overview

This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below). The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincaré sections, and return maps.

Product Details

ISBN-13:
9780738200903
Publisher:
Westview Press
Publication date:
08/04/1999
Series:
Studies in Nonlinearity Series
Pages:
256
Product dimensions:
6.38(w) x 9.58(h) x 0.72(d)

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