Exploring Chaos (Paperback: Reprint: 256 pages)
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Product Details: Exploring Chaos
| Author: | Brian Davies |
| Format: | Paperback: Reprint: 256 pages. |
| Publisher: | Westview Pr (10/01/2003) |
| ISBN: | 0813341272 |
| ISBN13: | 9780813341279 |
| Reading Level: |
Publisher Notes: Exploring Chaos
- An exciting new way of teaching chaos in dynamical systems to undergraduates, using a combination of text and computer experiments.
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, 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.
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