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  • Textbook
  • © 2007

Dynamical Systems with Applications using Mathematica®

Birkhäuser

Authors:

  • Book has a very hands-on approach and takes the reader from basic theory to recently published research material
  • Exercises are included at the end of every chapter
  • Applications to many disciplines: biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks
  • The introductory chapter provides complete tutorials on how to use Mathematica’s text-based input commands and palettes
  • Some of the topics presented are scarcely covered elsewhere
  • For a broad interdisciplinary readership of undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering
  • Working Mathematica notebooks available at http://library.wolfram.com/infocenter/Books/AppliedMathematics.

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XV
  2. A Tutorial Introduction to Mathematica

    • Stephen Lynch
    Pages 1-15
  3. Differential Equations

    • Stephen Lynch
    Pages 17-39
  4. Planar Systems

    • Stephen Lynch
    Pages 41-68
  5. Interacting Species

    • Stephen Lynch
    Pages 69-83
  6. Limit Cycles

    • Stephen Lynch
    Pages 85-109
  7. Bifurcation Theory

    • Stephen Lynch
    Pages 127-143
  8. Local and Global Bifurcations

    • Stephen Lynch
    Pages 195-215
  9. Linear Discrete Dynamical Systems

    • Stephen Lynch
    Pages 241-259
  10. Nonlinear Discrete Dynamical Systems

    • Stephen Lynch
    Pages 261-292
  11. Complex Iterative Maps

    • Stephen Lynch
    Pages 293-303
  12. Electromagnetic Waves and Optical Resonators

    • Stephen Lynch
    Pages 305-330
  13. Fractals and Multifractals

    • Stephen Lynch
    Pages 331-361
  14. Chaos Control and Synchronization

    • Stephen Lynch
    Pages 363-385
  15. Neural Networks

    • Stephen Lynch
    Pages 387-419
  16. Examination-Type Questions

    • Stephen Lynch
    Pages 421-427

About this book

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.

Reviews

From the reviews:

"Stephen Lynch's book offers a comprehensive introduction to the theory and application of differential equations and dynamical systems methods. Its focus on applications and avoidance of overly technical arguments makes it a an equally good choice for teaching an undergraduate course in dynamical systems, as self-study for graduate students interested in dynamical systems, or as an introductory text for researchers seeking an overview of some current developments in applied dynamical systems. Most importantly, its content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place.—Dynamical Systems Magazine

"This accessible university text shows how a wide range of differential equations work and begin to fail to work over a very wide range of solved and unsolvable applications. Mathematica is used throughout, from its tutorial introduction in Chapter 0 to the minimally chaotic neuromodule of the final section. This is the first work I have seen in which genuine self-education by computer is expected of the reader. The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.Datafile, The Journal of the HPCC

“The book is a good introduction to dynamical systems theory. … This book presents an original, cheap and powerful solution to the problem of analysis of large data sets. … The text is aimed at graduate students and working scientists in various branches of applied mathematics, natural sciences and engineering. … recommend ‘Dynamical Systems with Applications using MATHEMATICA®’ as a good handbook for a diverse readership, for graduates and professionals in mathematics, physics, science and engineering.” (Damian Trif, Studia Universitatis Babeş-Bolyai. Mathematica, Vol. LIV (4), December,2009)

Authors and Affiliations

  • Department of Computing and Mathematics, Manchester Metropolitan University, Manchester M1 5GD, United Kingdom

    Stephen Lynch

Bibliographic Information

Buy it now

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access