Dynamical Systems with Applications using Maple¿ [2 ed.] 9780817643898, 0817643893
"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to
242 22 5MB
English Pages 500 [510] Year 2010
Table of contents :
Front Matter....Pages i-xv
A Tutorial Introduction to Maple....Pages 1-15
Differential Equations....Pages 17-42
Planar Systems....Pages 43-69
Interacting Species....Pages 71-85
Limit Cycles....Pages 87-111
Hamiltonian Systems, Lyapunov Functions, and Stability....Pages 113-127
Bifurcation Theory....Pages 129-145
Three-Dimensional Autonomous Systems and Chaos....Pages 147-171
Poincaré Maps and Nonautonomous Systems in the Plane....Pages 173-196
Local and Global Bifurcations....Pages 197-218
The Second Part of Hilbert’s Sixteenth Problem....Pages 219-241
Linear Discrete Dynamical Systems....Pages 243-261
Nonlinear Discrete Dynamical Systems....Pages 263-295
Complex Iterative Maps....Pages 297-307
Electromagnetic Waves and Optical Resonators....Pages 309-335
Fractals and Multifractals....Pages 337-370
Chaos Control and Synchronization....Pages 371-393
Neural Networks....Pages 395-426
Simulation....Pages 427-444
Examination-Type Questions....Pages 445-451
Solutions to Exercises....Pages 453-474
Back Matter....Pages 1-35
Front Matter....Pages i-xv
A Tutorial Introduction to Maple....Pages 1-15
Differential Equations....Pages 17-42
Planar Systems....Pages 43-69
Interacting Species....Pages 71-85
Limit Cycles....Pages 87-111
Hamiltonian Systems, Lyapunov Functions, and Stability....Pages 113-127
Bifurcation Theory....Pages 129-145
Three-Dimensional Autonomous Systems and Chaos....Pages 147-171
Poincaré Maps and Nonautonomous Systems in the Plane....Pages 173-196
Local and Global Bifurcations....Pages 197-218
The Second Part of Hilbert’s Sixteenth Problem....Pages 219-241
Linear Discrete Dynamical Systems....Pages 243-261
Nonlinear Discrete Dynamical Systems....Pages 263-295
Complex Iterative Maps....Pages 297-307
Electromagnetic Waves and Optical Resonators....Pages 309-335
Fractals and Multifractals....Pages 337-370
Chaos Control and Synchronization....Pages 371-393
Neural Networks....Pages 395-426
Simulation....Pages 427-444
Examination-Type Questions....Pages 445-451
Solutions to Exercises....Pages 453-474
Back Matter....Pages 1-35
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