This

*Mathematica* book provides an introduction to dynamical systems theory, treating both continuous and discrete dynamical systems from basic theory to recently published research material. It includes approximately 400 illustrations, over 400 examples from a broad range of disciplines, and exercises with solutions, as well as an introductory

*Mathematica* tutorial and numerous simple

*Mathematica* programs throughout the text.

The volume is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering.

The attached notebook has been updated for

*Mathematica* 10.

A Tutorial Introduction to

*Mathematica* | Differential Equations | Planar Systems | Interacting Species | Limit Cycles | Hamiltonian Systems, Lyapunov Functions, and Stability | Bifurcation Theory | Three-Dimensional Autonomous Systems and Chaos | Poincaré Maps and Nonautonomous Systems in the Plane | Local and Global Bifurcations | The Second Part of Hilbert's Sixteenth Problem | Linear Discrete Dynamical Systems | Nonlinear Discrete Dynamical Systems | Complex Iterative Maps | Electromagnetic Waves and Optical Resonators | Fractals and Multifractals | Chaos Control and Synchronization | Neural Networks | Examination-Type Questions | Solutions to Exercises | References |

*Mathematica* Program Index

Applied Mathematics,

Calculus and Analysis,

Differential Equations,

Engineering,

Life Sciences,

Physics