This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks.

The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work.

Working Mathematica notebooks will be available at

http://library.wolfram.com/infocenter/Books/AppliedMathematics/.

Inhalt

Preface A Tutorial Introduction to Mathematica Differential Equations Planar Systems Interacting Species Limit Cycles Hamiltonian Systems, Lyapunov Functions, and Stability Bifurcation Theory Three-Dimensional Autonomous Systems and Chaos Poincaré 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 Examination-Type Questions Solutions to Exercises References Mathematica Program Index Index