Dynamical Systems with Applications using Mathematica®

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Springer Science & Business Media, Oct 1, 2007 - Mathematics - 484 pages
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This book provides an introduction to the theory of dynamical systems with the ® aid of the Mathematica computer algebra system. It is written for both senior undergraduates and graduate students. The ?rst part of the book deals with c- tinuous systems using ordinary differential equations (Chapters 1–10), the second part is devoted to the study of discrete dynamical systems (Chapters 11–15), and Chapters 16 and 17 deal with both continuous and discrete systems. It should be pointedoutthatdynamicalsystemstheoryisnotlimitedtothesetopicsbutalso- compassespartialdifferentialequations,integralandintegrodifferentialequations, stochastic systems, and time-delay systems, for instance. References [1]–[4] given at the end of the Preface provide more information for the interested reader. The author has gone for breadth of coverage rather than ?ne detail and theorems with proofs are kept at a minimum. The material is not clouded by functional analytic and group theoretical de?nitions, and so is intelligible to readers with a general mathematical background. Some of the topics covered are scarcely covered el- where. Most of the material in Chapters 9, 10, 14, 16, and 17 is at a postgraduate levelandhasbeenin?uencedbytheauthor’sownresearchinterests. Thereismore 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 ref- ence 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.
 

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Contents

0
1
Mathematica Program Index
2
Differential Equations
16
Planar Systems
41
1
69
4
84
6
126
8
170
Fractals and Multifractals
331
Chaos Control and Synchronization
363
6
369
17
386
4
408
6
415
18
421
2
424

Local and Global Bifurcations
195
5
204
The Second Part of Hilberts Sixteenth Problem
217
5
223
11
240
12
261
4
267
Complex Iterative Maps
293
Electromagnetic Waves and Optical Resonators
304
25
428
1
431
29
439
32
463
35
476
217
478
348
479
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