contents.txt

《Dynamical Systems with Applications using MATLAB》源代码

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% DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB %
% COPYRIGHT BIRKHAUSER 2004    STEPHEN LYNCH       %
% PUBLISHED June 2004                              %
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CONTENTS

Preface

0. A Tutorial Introduction to MATLAB and the Symbolic Math Toolbox
           0.1 Tutorial One: The Basics and the Symbolic Math Toolbox (1 Hour) 
	   0.2 Tutorial Two: Plots and Differential Equations (1 Hour) 
           0.3 MATLAB Program Files, or M-Files 
           0.4 Hints for Programming 
           0.5 MATLAB Exercises 
           
1. Linear Discrete Dynamical Systems
           1.1 Recurrence Relations 
           1.2 The Leslie Model
           1.3 Harvesting and Culling Policies
           1.4 MATLAB Commands
           1.5 Exercises 
           
2. Nonlinear Discrete Dynamical Systems
           2.1 The Tent Map and Graphical Iterations 
           2.2 Fixed Points and Periodic Orbits 
           2.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum Number 
           2.4 Gaussian and Henon Maps 
	   2.5 Applications
           2.6 MATLAB Commands 
           2.7 Exercises
           
3. Complex Iterative Maps
           3.1 Julia Sets and the Mandelbrot Set 
           3.2 Boundaries of Periodic Orbits 
           3.3 MATLAB Commands 
           3.4 Exercises
           
4. Electromagnetic Waves and Optical Resonators
            4.1 Maxwell's Equations and Electromagnetic Waves 
            4.2 Historical Background of Optical Resonators 
            4.3 The Nonlinear Simple Fibre Ring Resonator 
            4.4 Chaotic Attractors and Bistability 
            4.5 Linear Stability Analysis 
            4.6 Instabilities and Bistability 
            4.7 MATLAB Commands 
            4.8 Exercises 
            
5. Fractals and Multifractals
           5.1 Construction of Simple Examples 
           5.2 Calculating Fractal Dimensions
           5.3 A Multifractal Formalism 
           5.4 Multifractals in the Real World and Some Simple Examples 
           5.5 MATLAB Commands 
           5.6 Exercises 
           
6. Controlling Chaos
           6.1 Historical Background 
           6.2 Controlling Chaos in the Logistic Map 
           6.3 Controlling Chaos in the Henon Map 
           6.4 MATLAB Commands 
           6.5 Exercises 		   		   
           
7. Differential Equations
           7.1 Simple Differential Equations and Applications 
           7.2 Applications to Chemical Kinetics 
           7.3 Applications to Electric Circuits 
           7.4 Existence and Uniqueness Theorem 
           7.5 MATLAB Commands
           7.6 Exercises
           
8. Planar Systems
           8.1 Canonical Forms 
           8.2 Eigenvectors Defining Stable and Unstable Manifolds 
           8.3 Phase Portraits of Linear Systems in the Plane 
           8.4 Linearization and Hartman's Theorem 
           8.5 Constructing Phase Plane Diagrams 
           8.6 MATLAB Commands 
           8.7 Exercises 
           
9. Interacting Species
           9.1 Competing Species 
           9.2 Predator-Prey Models 
           9.3 Other Characteristics Affecting Interacting Species 
           9.4 MATLAB Commands
           9.5 Exercises 
           
10. Limit Cycles
           10.1 Historical Background 
           10.2 Existence and Uniqueness of Limit Cycles in the Plane 
           10.3 Non-Existence of Limit Cycles in the Plane 
           10.4 Exercises 
           
11. Hamiltonian Systems, Lyapunov Functions, and Stability
           11.1 Hamiltonian Systems in the Plane 
           11.2 Lyapunov Functions and Stability  
           11.3 MATLAB Commands  
           11.4 Exercises 
           
12. Bifurcation Theory
           12.1 Bifurcations of Nonlinear Systems in the Plane 
           12.2 Multistability and Bistability 
           12.3 MATLAB Commands 
           12.4 Exercises
           
13. Three-Dimensional Autonomous Systems and Chaos
           13.1 Linear Systems and Canonical Forms
           13.2 Nonlinear Systems and Stability 
           13.3 The Rossler System and Chaos 
           13.4 The Lorenz Equations, Chua's Circuit, and the Belousov-Zhabotinski Reaction 
           13.5 MATLAB Commands 
           13.6 Exercises 
           
14. Poincare Maps and Nonautonomous Systems in the Plane       
           14.1 Poincare Maps 
           14.2 Hamiltonian Systems with Two Degrees of Freedom   
           14.3 Nonautonomous Systems in the Plane 
           14.4 MATLAB Commands 
           14.5 Exercises
           
15. Local and Global Bifurcations
           15.1 Small-Amplitude Limit Cycle Bifurcations 
           15.2 Melnikov Integrals and Bifurcating Limit Cycles from a Center
           15.3 Homoclinic Bifurcations 
           15.4 MATLAB Commands
           15.5 Exercises 
           
16. The Second Part of David Hilbert's 16'th Problem
           16.1 Statement of Problem and Main Results 
           16.2 Poincare Compactification 
           16.3 Global Results for Lienard Systems 
           16.4 Local Results for Lienard Systems 
           16.5 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 MATLAB Commands 
           17.6 Exercises    
           
18. SIMULINK
           18.1 Introduction
           18.2 Electric Circuits 
           18.3 Mechanical Systems 
           18.4 Nonlinear Optics 
           18.5 The Lorenz System and Chaos Synchronization
           18.6 Exercises
           
19. Solutions to Exercises  

References
           Textbooks         
           Research Papers  
           
MATLAB Program File Index

Simulink Model File Index

Index