Lynch_2007 Dynamical Systems with Applications using MATLAB.rar

Dynamical Systems with Applications using MATLAB

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

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