Dynamical Systems with Applications using MATLAB, 2nd Edition

This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB^®, Simulink^®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD.

Features new to the second edition include

• sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization;
• chapters on image processing and binary oscillator computing;
• hundreds of new illustrations, examples, and exercises with solutions; and
• over eighty up-to-date MATLAB program files and Simulink model files available online. These files were voted MATLAB Central Pick of the Week in July 2013.

The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics.

Praise for the first edition

Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing.

―OR News/Operations Research Spectrum

The MATLAB programs are kept as simple as possible and the author’s experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes…. I recommend ‘Dynamical Systems with Applications using MATLAB’ as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering.

―Mathematica

Table of Contents

Chapter 1 A Tutorial Introduction to MATLAB
Chapter 2 Linear Discrete Dynamical Systems
Chapter 3 Nonlinear Discrete Dynamical Systems
Chapter 4 Complex Iterative Maps
Chapter 5 Electromagnetic Waves and Optical Resonators
Chapter 6 Fractals and Multifractals
Chapter 7 The Image Processing Toolbox
Chapter 8 Differential Equations
Chapter 9 Planar Systems
Chapter 10 Interacting Species
Chapter 11 Limit Cycles
Chapter 12 Hamiltonian Systems, Lyapunov Functions, and Stability
Chapter 13 Bifurcation Theory
Chapter 14 Three-Dimensional Autonomous Systems and Chaos
Chapter 15 Poincaré Maps and Nonautonomous Systems in the Plane
Chapter 16 Local and Global Bifurcations
Chapter 17 The Second Part of Hilbert’s Sixteenth Problem
Chapter 18 Neural Networks
Chapter 19 Chaos Control and Synchronization
Chapter 20 Binary Oscillator Computing
Chapter 21 Simulink
Chapter 22 Examination-Type Questions
Chapter 23 Solutions to Exercises