本资源为Dynamical Systems with Applications Using MATLAB一书（作者：S. Lynch, 2007年出版），提供了使用MATLAB进行动力系统应用研究的理论与实践指导。
Dynamical Systems with Applications using MATLAB
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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
- Section 0.1: The Basics and the Symbolic Math Toolbox (Duration: 1 Hour)
- Section 0.2: Plots and Differential Equations (Duration: 1 Hour)
- Section 0.3: MATLAB Program Files, or M-Files
- Section 0.4: Hints for Programming
- Section 0.5: MATLAB Exercises
1. Linear Discrete Dynamical Systems
- Chapter 1.1: Recurrence Relations
- Chapter 1.2: The Leslie Model
- Chapter 1.3: Harvesting and Culling Policies
- Chapter 1.4: MATLAB Commands
- Section 1.5 Exercises
2. Nonlinear Discrete Dynamical Systems
- Chapter 2.1: The Tent Map and Graphical Iterations
- Chapter 2.2: Fixed Points and Periodic Orbits
- Chapter 2.3: The Logistic Map, Bifurcation Diagram, and Feigenbaum Number
- Chapter 2.4: Gaussian and Henon Maps
- Section 2.5 Applications
- Section 2.6 MATLAB Commands
- Section 2.7 Exercises
3. Complex Iterative Maps
- Chapter 3.1: Julia Sets and the Mandelbrot Set
- Chapter 3.2: Boundaries of Periodic Orbits
- Section 3.3 MATLAB Commands
- Section 3.4 Exercises
4. Electromagnetic Waves and Optical Resonators
- Chapter 4.1: Maxwells Equations and Electromagnetic Waves
- Chapter 4.2: Historical Background of Optical Resonators
- Chapter 4.3: The Nonlinear Simple Fibre Ring Resonator
- Chapter 4.4: Chaotic Attractors and Bistability
- Chapter 4.5: Linear Stability Analysis
- Chapter 4.6: Instabilities and Bistability
- Section 4.7 MATLAB Commands
- Section 4.8 Exercises
5. Fractals and Multifractals
- Chapter 5.1: Construction of Simple Examples
- Chapter 5.2: Calculating Fractal Dimensions
- Chapter 5.3: A Multifractal Formalism
- Chapter 5.4: Multifractals in the Real World and Some Simple Examples
- Section 5.5 MATLAB Commands
- Section 5.6 Exercises
6. Controlling Chaos
- Chapter 6.1: Historical Background
- Chapter 6.2: Controlling Chaos in the Logistic Map
- Chapter 6.3: Controlling Chaos in the Henon Map
- Section 6.4 MATLAB Commands
- Section 6.5 Exercises
7. Differential Equations
- Chapter 7.1: Simple Differential Equations and Applications
- Chapter 7.2: Applications to Chemical Kinetics
- Chapter 7.3: Applications to Electric Circuits
- Chapter 7.4: Existence and Uniqueness Theorem
- Section 7.5 MATLAB Commands
- Section 7.6 Exercises
8. Planar Systems
- Chapter 8.1: Canonical Forms
- Chapter 8.2: Eigenvectors Defining Stable and Unstable Manifolds
- Chapter 8.3: Phase Portraits of Linear Systems in the Plane
- Chapter 8.4: Linearization and Hartmans Theorem
- Chapter 8.5: Constructing Phase Plane Diagrams
- Section 8.6 MATLAB Commands
- Section 8.7 Exercises
9. Interacting Species
- Chapter 9.1: Competing Species
- Chapter 9.2: Predator-Prey Models
- Chapter 9.3: Other Characteristics Affecting Interacting Species
- Section 9.4 MATLAB Commands
- Section 9.5 Exercises
10. Limit Cycles
- Chapter 10.1: Historical Background
- Chapter 10.2: Existence and Uniqueness of Limit Cycles in the Plane
- Chapter 10.3: Non-Existence of Limit Cycles in the Plane
- Section 10
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