Dynamical Systems with Applications Using Mathematica®

This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material.

Fully updated to recent versions of Mathematica

Book has a very hands-on approach and takes the reader from basic theory to modern research

Exercises are included at the end of every chapter

Applications to many disciplines: biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks

Fully updated to recent versions of Mathematica Book has a very hands-on approach and takes the reader from basic theory to modern research Exercises are included at the end of every chapter Applications to many disciplines: biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks Includes supplementary material: sn.pub/extras

Autorentext

Stephen Lynch is Senior Lecturer in the Department of Computing and Mathematics at Manchester Metropolitan University.

Also by the author:

Dynamical Systems with Applications using Maple™, ISBN 978-0-8176-4389-8

Dynamical Systems with Applications using MATLAB®, ISBN 978-3-319-06819-0

Zusammenfassung

Fully updated to recent versions of Mathematica

Book has a very hands-on approach and takes the reader from basic theory to modern research

Exercises are included at the end of every chapter

Applications to many disciplines: biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks

Inhalt

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.