"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(TM) 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. This text is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

Klappentext

Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter)

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

Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science

Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering

A hands-on approach is used with 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 with additional applications and further links of interest at Maplesoft's Application Center

Inhalt

A Tutorial Introduction to Maple.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincar#x00E9; Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert#x2019;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.- Simulation.- Examination-Type Questions.- Solutions to Exercises.