Exploring Chaos

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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. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software.
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Editorial Reviews

Booknews
Chaos theory is not just of interest to the physical sciences. Davies (mathematics, Australian National U.) introduces the theory of chaos (including fractals) in non-linear dynamic systems coupled with numerical and graphical representation, without resorting to advanced calculus and algebra. Appendices provide documentation for Chaos for Java software, a discussion of computing various types of equations, and a list of dimensional maps. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780813341279
  • Publisher: Westview Press
  • Publication date: 9/19/2003
  • Series: Studies in Nonlinearity Series
  • Edition description: REV
  • Pages: 256
  • Product dimensions: 6.00 (w) x 8.90 (h) x 0.70 (d)

Meet the Author


Brian Davies is a Professor of Mathematics at the Australian National University in Canberra, ACT. His research interests include exactly integrable non-linear quantum systems, lattice statistical mechanics, non-linear dynamical systems and chaos, and the use of computers in teaching. He has been a visiting fellow at Oxford University, Bristol University, and the Free University (Berlin). He has published many articles in his field.
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Table of Contents

1 Introduction 1
2 Orbits of one-dimensional systems 13
3 Bifurcations in one-dimensional systems 65
4 Two-dimensional systems 107
5 Fractals 147
6 Non-linear oscillations 177
A Chaos for Java Software 197
B Discrete Fourier Transform 221
C Variational equations 225
D List of Maps and Differential Equations 227
Bibliography 229
Index 232
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