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Book Table of Contents.txt
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB 2nd Edition %
% COPYRIGHT SPRINGER/BIRKHAUSER 2014 STEPHEN LYNCH %
% BOOK PUBLISHED USING R2015a %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
TABLE OF CONTENTS
Preface
1. A Tutorial Introduction to MATLAB and the Symbolic Math Toolbox
1.1 Tutorial One: The Basics and the Symbolic Math Toolbox (1 Hour)
1.2 Tutorial Two: Plots and Differential Equations (1 Hour)
1.3 MATLAB Program Files, or M-Files
1.4 Hints for Programming
1.5 MATLAB Exercises
2. Linear Discrete Dynamical Systems
2.1 Recurrence Relations
2.2 The Leslie Model
2.3 Harvesting and Culling Policies
2.4 MATLAB Commands
2.5 Exercises
3. Nonlinear Discrete Dynamical Systems
3.1 The Tent Map and Graphical Iterations
3.2 Fixed Points and Periodic Orbits
3.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum Number
3.4 Gaussian and Hénon Maps
3.5 Applications
3.6 MATLAB Commands
3.7 Exercises
4. Complex Iterative Maps
4.1 Julia Sets and the Mandelbrot Set
4.2 Boundaries of Periodic Orbits
4.3 MATLAB Commands
4.4 Exercises
5. Electromagnetic Waves and Optical Resonators
5.1 Maxwell's Equations and Electromagnetic Waves
5.2 Historical Background
5.3 The Nonlinear Simple Fibre Ring Resonator
5.4 Chaotic Attractors and Bistability
5.5 Linear Stability Analysis
5.6 Instabilities and Bistability
5.7 MATLAB Commands
5.8 Exercises
6. Fractals and Multifractals
6.1 Construction of Simple Examples
6.2 Calculating Fractal Dimensions
6.3 A Multifractal Formalism
6.4 Multifractals in the Real World and Some Simple Examples
6.5 MATLAB Commands
6.6 Exercises
7. The Image Processing Toolbox
7.1 Image Processing and Matrices
7.2 The Fast Fourier Transform
7.3 The Fast Fourier Transform on Images
7.4 Exercises
8. Differential Equations
8.1 Simple Differential Equations and Applications
8.2 Applications to Chemical Kinetics
8.3 Applications to Electric Circuits
8.4 Existence and Uniqueness Theorem
8.5 MATLAB Commands
8.6 Exercises
9. Planar Systems
9.1 Canonical Forms
9.2 Eigenvectors Defining Stable and Unstable Manifolds
9.3 Phase Portraits of Linear Systems in the Plane
9.4 Linearization and Hartman's Theorem
9.5 Constructing Phase Plane Diagrams
9.6 MATLAB Commands
9.7 Exercises
10. Interacting Species
10.1 Competing Species
10.2 Predator-Prey Models
10.3 Other Characteristics Affecting Interacting Species
10.4 MATLAB Commands
10.5 Exercises
11. Limit Cycles
11.1 Historical Background
11.2 Existence and Uniqueness of Limit Cycles in the Plane
11.3 Non-Existence of Limit Cycles in the Plane
11.4 Perturbation Methods
11.5 MATLAB Commands
11.6 Exercises
12. Hamiltonian Systems, Lyapunov Functions, and Stability
12.1 Hamiltonian Systems in the Plane
12.2 Lyapunov Functions and Stability
12.3 MATLAB Commands
12.4 Exercises
13. Bifurcation Theory
13.1 Bifurcations of Nonlinear Systems in the Plane
13.2 Normal Forms
13.3 Multistability and Bistability
13.4 MATLAB Commands
13.5 Exercises
14. Three-Dimensional Autonomous Systems and Chaos
14.1 Linear Systems and Canonical Forms
14.2 Nonlinear Systems and Stability
14.3 The Rössler System and Chaos
14.4 The Lorenz Equations, Chua's Circuit, and the Belousov-Zhabotinski Reaction
14.5 MATLAB Commands
14.6 Exercises
15. Poincaré Maps and Nonautonomous Systems in the Plane
15.1 Poincaré Maps
15.2 Hamiltonian Systems with Two Degrees of Freedom
15.3 Nonautonomous Systems in the Plane
15.4 MATLAB Commands
15.5 Exercises
16. Local and Global Bifurcations
16.1 Small-Amplitude Limit Cycle Bifurcations
16.2 Gröbner Bases
16.3 Melnikov Integrals and Bifurcating Limit Cycles from a Center
16.4 Homoclinic Bifurcations
16.5 MATLAB and MuPAD Commands
16.6 Exercises
17. The Second Part of David Hilbert's 16'th Problem
17.1 Statement of Problem and Main Results
17.2 Poincaré Compactification
17.3 Global Results for Liénard Systems
17.4 Local Results for Liénard Systems
17.5 Exercises
18. Neural Networks
18.1 Introduction
18.2 The Delta Learning Rule and Backpropagation
18.3 The Hopfield Network and Lyapunov Stability
18.4 Neurodynamics
18.5 MATLAB Commands
18.6 Exercises
19. Chaos Control and Synchronization
19.1 Historical Background
19.2 Controlling Chaos in the Logistic Map
19.3 Controlling Chaos in the Hénon Map
19.4 Chaos Synchronization
19.5 MATLAB Commands
19.6 Exercises
20. Binary Oscillator Computing
20.1 Brain Inspired Computing
20.2 Oscillatory Threshold Logic
20.3 Applications and Future Work
20.4 MATLAB Commands
20.5 Exercises
21. SIMULINK
21.1 Introduction
21.2 Electric Circuits
21.3 A Mechanical System
21.4 Nonlinear Optics
21.5 The Lorenz System and Chaos Synchronization
21.6 Exercises
22. Examination-Type Questions
22.1 Examination 1
22.2 Examination 2
22.3 Examination 3
23. Solutions to Exercises
References
Textbooks
Research Papers
MATLAB Program File Index
Simulink Model File Index
Index