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Numerical Continuation Methods for Dynamical Systems : Path following and boundary value problems - Bernd Krauskopf

Numerical Continuation Methods for Dynamical Systems

Path following and boundary value problems

By: Bernd Krauskopf (Editor), Hinke M. Osinga (Editor), Jorge Galan-Vioque (Editor)

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Published: 1st September 2007
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Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation.

This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve.

The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

A Continuing Influence in Dynamicsp. V
Forewordp. IX
Lecture Notes on Numerical Analysis of Nonlinear Equationsp. 1
Interactive Continuation Toolsp. 51
Higher-Dimensional Continuationp. 77
Computing Invariant Manifolds via the Continuation of Orbit Segmentsp. 117
The Dynamics of SQUIDs and Coupled Pendulap. 155
Global Bifurcation Analysis in Laser Systemsp. 177
Numerical Bifurcation Analysis of Electronic Circuitsp. 221
Periodic Orbit Continuation in Multiple Time Scale Systemsp. 253
Continuation of Periodic Orbits in Symmetric Hamiltonian Systemsp. 269
Phase Conditions, Symmetries and PDE Continuationp. 301
Numerical Computation of Coherent Structuresp. 331
Continuation and Bifurcation Analysis of Delay Differential Equationsp. 359
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781402063558
ISBN-10: 1402063555
Series: Understanding Complex Systems
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 399
Published: 1st September 2007
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.79