Dynamical Systems with Applications using Mathematica®

✍ Scribed by Stephen Lynch

• Publisher: Birkhäuser Boston
• Year: 2007
• Tongue: English
• Leaves: 497
• Edition: 1
• Category: Library

✦ Synopsis

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. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.

✦ Table of Contents

Contents......Page 4
Preface......Page 9
0 - ATutorial Introduction to Mathematica......Page 15
1 - Differential Equations......Page 31
2 - Planar Systems......Page 55
3 - Interacting Species......Page 83
4 - Limit Cycles......Page 99
5 - Hamiltonian Systems, LyapunovFunctions, and Stability......Page 125
6 - Bifurcation Theory......Page 141
7 - Three-Dimensional AutonomousSystems and Chaos......Page 159
8 - Poincaré Maps and NonautonomousSystems in the Plane......Page 185
9 -
Local and Global Bifurcations......Page 209
10 -
The Second Part of Hilbert’sSixteenth Problem......Page 231
11 -
Linear Discrete Dynamical Systems......Page 255
12 -
Nonlinear Discrete DynamicalSystems......Page 275
13 - Complex Iterative Maps......Page 307
14 - ElectromagneticWaves and OpticalResonators......Page 319
15 - Fractals and Multifractals......Page 345
16 - Chaos Control and Synchronization......Page 377
17 - Neural Networks......Page 401
18 - Examination-Type Questions......Page 435
19 - Solutions to Exercises......Page 443
Textbooks......Page 465
Research Papers......Page 473
Mathematica Program Index......Page 483
Index......Page 486