Synopses & Reviews
"""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. MAPLE plots with simple commands and programs are listed at the end of each chapter, and along with figures can be viewed at the website http://www.birkhauser.com/cgi-win/ISBN/0-8176-4150-5. Additional applications and further links of interest can be found at http://www.maplesoft.com. 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."
Review
"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®. U.K. Nonlinear News 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. The first portion of the book uses differential equations to model examples taken from various topics such as mechanical systems, chemical kinetics, electric circuits, interacting species and economics. Both real and complex discrete dynamical systems are considered in the second half of the text, and examples are taken from economics, population dynamics, nonlinear optics and materials science. Common themes such as bifurcation, bistability, chaos, instability, multistability and periodicity run through several chapters of the book. Lynch gives good Maple routines for drawing cobweb and bifurcation diagrams, Julia sets and the ubiquitous Mandelbrot set. A couple of chapters on fractals introduce the concepts of self-similarity, box-counting dimension and even the spectrum of dimensions for multifractals. The control of chaos is also discussed, and an algorithm for the OGY method is given. This publication will provide a solid basis for both research and education in nonlinear dynamical systems. The Maple Reporter"
Synopsis
This introduction to the theory of dynamical systems utilizes MAPLE to facilitate the understanding of the theory and to deal with the examples, diagrams, and exercises. A wide range of topics in differential equations and discrete dynamical systems is discussed with examples drawn from many different areas of application, including mechanical systems and materials science, electronic circuits and nonlinear optics, chemical reactions and meteorology, and population modeling.
Synopsis
Preface * A Tutorial Introduction to Maple Toolbox * Differential Equations * Planar Systems * Interacting Species * Limit Cycles * Hamiltonian Systems, Lyapunov Functions, and Stability * Bifurcation Theory * Three Dimensional Autonomous Systems and Chaos * Poincare Maps and Nonautonomous Systems in the Plane * Local and Global Bifurcations * The Second Part of David Hilbert's Sixteenth Problem * Linear Discrete Dynamical Systems * Nonlinear Discrete Dynamical Systems * Complex Iterative Maps * Electromagnetic Waves and Optical Resonators * Fractals and Multifractals * Chaos Control and Synchronization * Neural Networks * Maplets * Solutions to Exercises * References * Maple Program File Index * Maple File Index * Index