Dynamical Systems with Applications using Maple™

1. Front Matter

   Pages i-xv

   PDF

2. A Tutorial Introduction to Maple

   • Stephen Lynch

   Pages 1-15

3. Differential Equations

   • Stephen Lynch

   Pages 17-42

4. Planar Systems

   • Stephen Lynch

   Pages 43-69

5. Interacting Species

   • Stephen Lynch

   Pages 71-85

6. Limit Cycles

   • Stephen Lynch

   Pages 87-111

7. Hamiltonian Systems, Lyapunov Functions, and Stability

   • Stephen Lynch

   Pages 113-127

8. Bifurcation Theory

   • Stephen Lynch

   Pages 129-145

9. Three-Dimensional Autonomous Systems and Chaos

   • Stephen Lynch

   Pages 147-171

10. Poincaré Maps and Nonautonomous Systems in the Plane

    • Stephen Lynch

    Pages 173-196

11. Local and Global Bifurcations

    • Stephen Lynch

    Pages 197-218

12. The Second Part of Hilbert’s Sixteenth Problem

    • Stephen Lynch

    Pages 219-241

13. Linear Discrete Dynamical Systems

    • Stephen Lynch

    Pages 243-261

14. Nonlinear Discrete Dynamical Systems

    • Stephen Lynch

    Pages 263-295

15. Complex Iterative Maps

    • Stephen Lynch

    Pages 297-307

16. Electromagnetic Waves and Optical Resonators

    • Stephen Lynch

    Pages 309-335

17. Fractals and Multifractals

    • Stephen Lynch

    Pages 337-370

18. Chaos Control and Synchronization

    • Stephen Lynch

    Pages 371-393

19. Neural Networks

    • Stephen Lynch

    Pages 395-426

20. Simulation

    • Stephen Lynch

    Pages 427-444

Since the ?rst edition of this book was published in 2001, the algebraic computa- ™ tion package Maple has evolved from Maple V into Maple 13. 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 chapters on neural networks and simulation have been added. Therearealsonewsectionsonperturbationmethods,normalforms,Gröbnerbases, and chaos synchronization. This book provides an introduction to the theory of dynamical systems with the aid of the Maple algebraic manipulation package. 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 16–18 deal with both continuous and discrete systems. Chapter 19 lists examination-type questions used by the author over many years, one set to be used in a computer laboratory with access to Maple, and the other set to be used without access to Maple. Chapter 20 lists answers to all of the exercises given in the book. It should be pointed out that dynamical systems theory is not l- ited to these topics but also encompasses partial differential equations, integral and integro-differential equations, stochastic systems, and time delay systems, for instance. References [1]–[5] given at the end of the Preface provide more inf- mation for the interested reader.

• Chaos
• MATLAB
• Maple
• computer algebra
• electromagnetic wave
• linear optimization
• simulation
• ordinary differential equations

From the reviews of the second edition:

"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."   —UK Nonlinear News (1st Edition)

"This book covers standard material for an introduction to dynamical systems theory. Written for both advanced undergraduates and new postgraduate students, this book is split into two distinctive parts: continuous systems using ordinary differential equations and discrete dynamical systems. Lynch uses the Maple package as a tool throughout the text to help with the understanding of the subject. The book contains over 250 examples and exercises with solutions and takes a hands-on approach. There are over 300 individual figures including about 200 Maple plots, with simple commands and programs listed at the end of each chapter...This publication will provide a solid basis for both research and education in nonlinear dynamical systems."   —The Maple Reporter (1st Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."   —Mathematical Reviews (1st Edition)

"… a very nice tutorial on Maple in which quite a few mathematical and graphical commands are illustrated. A student could quickly work through this tutorial and then be ready to do quite a bit with Maple….[The second part of Hilbert’s 16^th problem] is not the topic encountered in most ODE texts, even if the question has been open for 100 years! …Lynch’s book provides great references, as well as Maple code that could be easily modified by readers who have the tools to quickly engage in quite sophisticated numerical experimentation."   —SIAM Review (1st Edition)

"A student or scientist, who works through some chapters of the book, learns a good deal about the presented mathematical concepts and possibilities of the symbolic algebra package to assist the researcher in understanding his mathematical model."  —Dynamical Systems Magazine (1st Edition)

“This book, that provides an introduction to the study of dynamical systems with the aid of the algebraic package Maple, is the second edition of the well known classical book of Stephen Lynch … . a well written and highly readable introduction to the numerical study dynamical systems with Maple at an introductory level that covers many topics of this subject and can be used as a very valuable resource for many courses in applied mathematics and modelization in engineering and physical sciences.” (Manuel Calvo, Zentralblatt MATH, Vol. 1193, 2010)

• Dept. Computing & Mathematics, Manchester Metropolitan University, Manchester, United Kingdom

  Stephen Lynch

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