Dynamical Systems with Applications using Maple™

"Dynamical Systems with Applications using MAPLE" covers standard material for an introduction to dynamical systems theory. The text begins with a tutorial guide to MAPLE and thereafter is divided into two main areas: continuous systems using ordinary differential equations and discrete dynamical systems. In the first part of the text, differential equations are used to model examples taken from various disciplines, including mechanical systems, chemical kinetics, electric circuits, interacting species, and economics. In the second half, both real and complex discrete dynamical systems are considered and examples are taken from economics, population dynamics, nonlinear optics, and materials science.

Approximately 200 illustrations, over 250 examples, and exercises with solutions play a key role in the presentation. The book has a hands-on approach, using MAPLE as a tool throughout.Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. Some chapters deal with recently published research articles and provide a useful resource for open problems in nonlinear dynamical systems.

The text is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

"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 (Review of First 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 (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

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Also by the author:

Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica®, ISBN 978-0-8176-4482-6