Dynamical Systems with Applications using MATLAB / Edition 1

Dynamical Systems with Applications using MATLAB / Edition 1

by Stephen Lynch
     
 

ISBN-10: 0817643214

ISBN-13: 9780817643218

Pub. Date: 06/10/2004

Publisher: Birkhauser Verlag

This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox.

Beginning

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Overview

This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox.

Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems.

Approximately 330 illustrations, over 300 examples, and exercises with solutions play a key role in the presentation. Over 60 MATLAB® program files and Simulink® model files are listed throughout the text; these files may also be downloaded from the Internet at: http://www.mathworks.com/matlabcentral/fileexchange/. Additional applications and further links of interest are also available at the author's website.

The hands-on approach of Dynamical Systems with Applications using MATLAB® engages a wide audience of senior undergraduate and graduate students, applied mathematicians, engineers, and working scientists in various areas of the natural sciences.

Reviews of the author’s published book Dynamical Systems with Applications using Maple®:

"The text treats a remarkable spectrum of topics…and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple®." – U.K. Nonlinear News

"…will provide a solid basis for both research and education in nonlinear dynamical systems." – The Maple Reporter

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Product Details

ISBN-13:
9780817643218
Publisher:
Birkhauser Verlag
Publication date:
06/10/2004
Edition description:
2004
Pages:
459
Product dimensions:
0.97(w) x 6.14(h) x 9.21(d)

Table of Contents

A tutorial introduction to MATLAB and the symbolic math toolbox1
1Linear discrete dynamical systems15
2Nonlinear discrete dynamical systems35
3Complex iterative maps69
4Electromagnetic waves and optical resonators81
5Fractals and multifractals109
6Controlling chaos143
7Differential equations161
8Planar systems185
9Interacting species215
10Limit cycles229
11Hamiltonian systems, Lyapunov functions, and stability243
12Bifurcation theory257
13Three-dimensional autonomous systems and chaos271
14Poincare maps and nonautonomous systems in the plane297
15Local and global bifurcations323
16The second part of Hilbert's sixteenth problem335
17Neural networks359
18Simulink397
19Solutions to exercises409

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