Dynamical Systems with Applications using Mathematica®

Preface
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 David Hilbert's Sixteenth Problem
Linear Discrete Dynamical Systems
Nonlinear Discrete Dynamical Systems
Complex Iterative Maps
Electromagnetic Waves and Optical ResonatorsFractals and Multifractals
Chaos Control and Synchronization
Neural Networks
Examination-Type Questions
Solutions to Exercises
References
Mathematica Program Index
Index

From the reviews: "Stephen Lynch's book offers a comprehensive introduction to the theory and application of differential equations and dynamical systems methods. Its focus on applications and avoidance of overly technical arguments makes it a an equally good choice for teaching an undergraduate course in dynamical systems, as self-study for graduate students interested in dynamical systems, or as an introductory text for researchers seeking an overview of some current developments in applied dynamical systems. Most importantly, its content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place.--Dynamical Systems Magazine "This accessible university text shows how a wide range of differential equations work and begin to fail to work over a very wide range of solved and unsolvable applications. Mathematica is used throughout, from its tutorial introduction in Chapter 0 to the minimally chaotic neuromodule of the final section. This is the first work I have seen in which genuine self-education by computer is expected of the reader. The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.--Datafile, The Journal of the HPCC "The book is a good introduction to dynamical systems theory. ! This book presents an original, cheap and powerful solution to the problem of analysis of large data sets. ! The text is aimed at graduate students and working scientists in various branches of applied mathematics, natural sciences and engineering. ! recommend 'Dynamical Systems with Applications using MATHEMATICA(R)' as a good handbook for a diverse readership, for graduates and professionals in mathematics, physics, science and engineering." (Damian Trif, Studia Universitatis BabeAu-Bolyai. Mathematica, Vol. LIV (4), December, 2009)