Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students

Description

Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations. Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities. In addition, readers will learn several concepts from the field of dynamical systems, including chaos theory, how systems depend on parameters, and how simple physical systems can lead to complicated behavior. XPPAUT is a tool for simulating, animating, and analyzing dynamical systems that evolved from tools developed by the author for studying nonlinear oscillations. XPPAUT offers several advantages over MATLAB, Maple, and Mathematica, including the following: 1) a faster way to numerically solve differential equations and do numerical integration; 2) more flexibility with integration, including interactive integration that allows the user to see the progress of the solution as it is computed; 3) an interface with AUTO, a continuation package; 4) simpler syntax for setting up differentiation equations; and 5) free downloading of the source code Audience This book will be most useful to researchers and modelers who want to simulate and analyze a system, and to students as an adjunct to a class in modeling or differential equations.