Preface to Dynamical Systems with Applications using MATLAB
Since the first printing of this book in 2004, MATLABR has evolved from MATLAB version 6 to MATLAB version R2014b, where presently, the package is updated twice a year. Accordingly, the second edition has been thoroughly updated and new material has been added. In this edition, there are many more applications, examples, and exercises, all with solutions, and new sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization have been added. There are also new chapters on image processing and binary oscillator computing. This book provides an introduction to the theory of dynamical systems with the aid of MATLAB, the Symbolic Math ToolboxTM, the Image Processing ToolboxTM, and SimulinkTM. It is written for both senior undergraduates and graduate students. Chapter 1 provides a tutorial introduction to MATLAB—new users should go through this chapter carefully whilst those moderately familiar and experienced users will find this chapter a useful source of reference. Chapters 2–7 deal with discrete systems, Chaps. 8–17 are devoted to the study of continuous systems using ordinary differential equations and Chaps. 18–21 deal with both continuous and discrete systems.
Chapter 22 lists three MATLAB-based examinations to be sat in a computer laboratory with access to MATLAB and Chap. 23 lists answers to all of the exercises given in the book. It should be pointed out that dynamical systems theory is not limited to these topics but also encompasses partial differential equations, integral and integro-differential equations, stochastic systems, and timedelay systems, for instance. References [1–5] given at the end of the Preface provide more information for the interested reader. The author has gone for breadth of coverage rather than fine detail and theorems with proofs are kept at a minimum. The material is not clouded by functional analytic and group theoretical definitions and so is intelligible to readers with a general mathematical background.
Some of the topics covered are scarcely covered elsewhere. Most of the material in Chaps. 7, 10, 11, 15–19, and 21 is at postgraduate level and has been influenced by the author’s own research interests. There is more theory in these chapters than in the rest of the book since it is not easily accessed anywhere else. It has been found that these chapters are especially useful as reference material for senior undergraduate project work. The theory in other chapters of the book is dealt with more comprehensively in other texts, some of which may be found in the references section of the corresponding chapter. The book has a very hands-on approach and takes the reader from the basic theory right through to recently published research material. MATLAB is extremely popular with a wide range of researchers from all sorts of disciplines, it has a very user-friendly interface and has extensive visualization and numerical computation capabilities. It is an ideal package to adopt for the study of nonlinear dynamical systems; the numerical algorithms work very quickly, and complex pictures can be plotted within seconds.
The Simulink accessory to MATLAB is used for simulating dynamical processes. It is as close as one can get to building apparatus and investigating the output for a given input without the need for an actual physical model. For this reason, Simulink is very popular in the field of engineering. Note that the latest student version of MATLAB comes with a generous additional ten toolboxes including the Symbolic Math Toolbox, the Image Processing Toolbox, and Simulink.
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