Preface
0 A Tutorial Introduction to Maple
0.1 A Quick Tour of Maple
0.2 Tutorial One: The Basics (One Hour)
0.3 Tutorial Two: Plots and Differential Equations (One Hour)
0.4 Simple Maple Programs
0.5 Hints for Programming
0.6 Maple Exercises
1 Differential Equations
1.1 Simple Differential Equations and Applications
1.2 Applications to Chemical Kinetics
1.3 Applications to Electric Circuits
1.4 Existence and Uniqueness Theorem
1.5 Maple Commands
1.6 Exercises
2 Planar Systems
2.1 Canonical Forms.
2.2 Eigenvectors Defining Stable and Unstable Mani/blds
2.3 Phase Portraits of Linear Systems in the Plane
2.4 Linearization and Hartman's Theorem
2.5 Constructing Phase Plane Diagrams
2.6 Maple Commands
2.7 Exercises
3 Interacting Species
3.1 Competing' Species
3.2 Predator-Prey Models
3.3 Other Characteristics Affecting Interacting Species
3.4 Maple Commands
3.5 Exercises
4 Limit Cycles
4.1 Historical Background
4.2 Existence and Uniqueness of Limit Cycles in the Plane
4.3 Nonexistence of Limit Cycles in the Plane
4.4 Perturbation Methods
4.5 Maple Commands
4.6 Exercises
5 Hamiltonian Systems, Lyapunov Functions, and Stability
5.1 Hamiltonian Systems in the Plane
5.2 Lyapunov Functions and Stability
5.3 Maple Commands
5.4 Exercises
6 Bifurcation Theory
6.1 Bifurcations of Nonlinear Systems in the Plane
6.2 Normal Forms
6.3 Multistability and Bistability
6.4 Maple Commands
6.5 Exercises
7 Three-Dimensional Autonomous Systems and Chaos
7.1 Linear Systems and Canonical Forms
7.2 Nonlinear Systems and Stability
7.3 The RSssler System and Chaos
7.4 The Lorenz Equations, Chua's Circuit, and the Belousov-Zhabotinski Reaction
7.5 Maple Commands :
7.6 Exercises
8 Poincare Maps and Nonautonomons Systems in the Plane
8. I Poincar6 Maps
8.2 Hamiltonian Systems with Two Degrees of Freedom
8.3 Nonautonomous Systems in the Plane
8.4 Maple Commands
8.5 Exercises
9 Local and Global Bifurcations
9.1 Small-Amplitude Limit Cycle Bifurcations
9.2 Gr6bner Bases
9.3 Melnikov Integrals and Bifurcating Limit Cycles from a Center
9.4 Bifurcations Involving Homoclinic Loops
9.5 Maple Commands
9.6 Exercises
10 The Second Part of Hilbert's Sixteenth Problem
10.1 Statement of Problem and Main Results
10.2 Poincar6 Compactification
10.3 Global Results for Li6nard Systems
10.4 Local Results for Li~nard Systems
10.5 Exercises
11 Linear Discrete Dynamical Systems
11.1 Recurrence Relations
11.2 The Leslie Model
11.3 Harvesting and Culling Policies
11.4 Maple Commands
11.5 Exercises
12 Nonlinear Discrete Dynamical Systems
12.1 The Tent Map and Graphical Iterations
12.2 Fixed Points and Periodic Orbits
12.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum Number
12.4 Gaussian and H4non Maps
12.5 Applications
12.6 Maple Commands
12.7 Exercises
13 Complex Iterative Maps
13.1 Julia Sets and the Mandelbrot Set
13.2 Boundaries of Periodic Orbits
13.3 Maple Commands
13.4 Exercises
14 Electromagnetic Waves and Optical Resonators
14.1 Maxweil's Equations and Electromagnetic Waves
14.2 Historical Background
14.3 The Nonlinear SFR Resonator
14.4 Chaotic Attractors and Bistability
14.5 Linear Stability Analysis
14.6 Instabilities and Bistability
14.7 Maple Commands
14.8 Exercises
15 Fractals and Multifractals
15.1 Construction of Simple Examples
15.2 Calculating Fractal Dimensions
15.3 A Multifractal Formalism
15.4 Multifractals in the Real World and Some Simple Examples
15.5 Maple Commands
15.6 Exercises
16 Chaos Control and Synchronization
16.1 Historical Background
16.2 Controlling Chaos in the Logistic Map
16.3 Controlling Chaos in the H~non Map
16.4 Chaos Synchronization
16.5 Maple Commands
16.6 Exercises
17 Neural Networks
17.1 Introduction
17.2 The Delta Learning Rule and Backpropagation
17.3 The Hopfield Network and Lyapunov Stability
17.4 Neurodynamics
17.5 Maple Commands
17.6 Exercises
18 Simulation
18.1 Simulink
18.2 The MapleSim Connectivity Toolbox
18.3 MapleSim
18.4 Exercises
19 Examination-Type Questions
19.1 Dynamical Systems with Applications
19.2 Dynamical Systems with Maple
20 Solutions to Exercises
20.0 Chapter 0
20.1 Chapter 1
20.2 Chapter 2
20.3 Chapter 3
20.4 Chapter 4
20.5 Chapter 5
20.6 Chapter 6
20.7 Chapter 7
20.8 Chapter 8
20.9 Chapter 9
20.10 Chapter 10
20.11 Chapter 11
20.12 Chapter 12
20.13 Chapter 13
20.14 Chapter 14
20.15 Chapter 15
20.16 Chapter 16
20.17 Chapter 17
20.18 Chapter 18
20.19 Chapter 19
References
Textbooks
Research Papers
Maple Program Index
Index
