"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

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.

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.

Inhalt

0 A Tutorial Introduction to Maple.- 1 Differential Equations.- 2 Linear Systems in the Plane.- 3 Nonlinear Systems in the Plane.- 4 Interacting Species.- 5 Limit Cycles.- 6 Hamiltonian Systems, Lyapunov Functions, and Stability.- 7 Bifurcation Theory.- 8 Three-Dimensional Autonomous Systems and Chaos.- 9 Poincaré Maps and Nonautonomous Systems in the Plane.- 10 Local and Global Bifurcations.- 11 The Second Part of David Hilbert's Sixteenth Problem.- 12 Limit Cycles of Liénard Systems.- 13 Linear Discrete Dynamical Systems.- 14 Nonlinear Discrete Dynamical Systems.- 15 Complex Iterative Maps.- 16 Electromagnetic Waves and Optical Resonators.- 17 Analysis of Nonlinear Optical Resonators.- 18 Fractals.- 19 Multifractals.- 20 Controlling Chaos.- 21 Examination-Type Questions.- 22 Solutions to Exercises.- References.- Textbooks.- Research Papers.