"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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