ISBN10: 0817641505
ISBN13: 9780817641504
Edition/Copyright: 01

Publisher: Birkhauser Boston, Inc.
Cover: Paperback
Year Published: 2001
Weight: 1.5lbs.
Used Condition: Good/Excellent

Dynamical Systems With Application Using Maple

by Stephen Lynch


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Summary

Table of Contents

"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.

Preface

Chapter 0. A Tutorial Introduction to MAPLE

1. Differential Equations

2. Linear Systems in the Plane

3. Nonlinear Systems in the Plane

4. Modelling Interacting Species

5. Limit Cycles

6. Hamiltonian Systems, Liapunov Functions and Stability

7. Bifurcation Theory

8. Three-Dimensional Autonomous Systems and Chaos

9. Poincar\' Maps and Non-Autonomous Systems in the Plane

10. Local and Global Bifurcations

11. The Second Part of David Hilbert's 16'th Problem

12. Limit Cycles of Li\' nard 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

Examination Type Questions I

Examination Type Questions II

Index

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Dynamical Systems With Application Using Maple

by Stephen Lynch


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