Dynamical Systems with Applications using MAPLE

Front Matter....Pages i-xiii
A Tutorial Introduction to Maple....Pages 1-11
Differential Equations....Pages 13-34
Linear Systems in the Plane....Pages 35-49
Nonlinear Systems in the Plane....Pages 51-64
Interacting Species....Pages 65-76
Limit Cycles....Pages 77-89
Hamiltonian Systems, Lyapunov Functions, and Stability....Pages 91-103
Bifurcation Theory....Pages 105-117
Three-Dimensional Autonomous Systems and Chaos....Pages 119-142
Poincaré Maps and Nonautonomous Systems in the Plane....Pages 143-167
Local and Global Bifurcations....Pages 169-180
The Second Part of David Hilbert’s Sixteenth Problem....Pages 181-192
Limit Cycles of Liénard Systems....Pages 193-204
Linear Discrete Dynamical Systems....Pages 205-222
Nonlinear Discrete Dynamical Systems....Pages 223-253
Complex Iterative Maps....Pages 255-265
Electromagnetic Waves and Optical Resonators....Pages 267-282
Analysis of Nonlinear Optical Resonators....Pages 283-294
Fractals....Pages 295-312
Multifractals....Pages 313-328
Controlling Chaos....Pages 329-345
Examination-Type Questions....Pages 347-351
Solutions to Exercises....Pages 353-373
Back Matter....Pages 375-399