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Full Description
This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system.
Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.
Contents
Preface
Author biography
Introduction
Phase-plane analysis
Stability analysis for ODEs
Introduction to bifurcations
Bifurcation analysis with AUTO
Invariant manifolds
Singular perturbation theory
Hamiltonian systems
Nonautonomous systems
Maps and differential equations
Maps: stability and bifurcation analysis
Delay-differential equations
Reaction-diffusion equations
Appendix A: Software installation
