Dynamical Systems with Applications using MATLAB®

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Springer Science & Business Media, Jun 10, 2004 - Technology & Engineering - 459 pages
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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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Contents

A Tutorial Introduction to M AIL AB and the Symbolic Math Toolbox
1
Linear Discrete Dynamical Systems
15
Nonlinear Discrete Dynamical Systems
35
Complex Iterative Maps
69
Electromagnetic Waves and Optical Resonators
81
Fractals and Multifractals
109
Controlling Chaos
143
Differential Equations
161
Bifurcation Theory
257
ThreeDimensional Autonomous Systems and Chaos
271
Poincare Maps and Nonautonomous Systems in the Plane
297
Local and Global Bifurcations
323
The Second Part of HilbertsSixteenth Problem
335
Neural Networks
359
Simulink
397
Solutions to Exercises
409

Planar Systems
185
Interacting Species
215
Limit Cycles
229
Hamiltonian Systems Lyapunov Functions and Stability
243

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