Overview
- An overview of the influence of an important tool for bifurcation analysis
- Providing this material, so far spread over a large body of research literature in different fields, in one single source
- Also accessible to non-specialists
- With 200 figures, 26 in full colour
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (12 chapters)
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Front Matter
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Numerical Continuation Methods for Dynamical Systems
Book Subtitle: Path following and boundary value problems
Editors: Bernd Krauskopf, Hinke M. Osinga, Jorge Galán-Vioque
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-1-4020-6356-5
Publisher: Springer Dordrecht
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media B.V. 2007
Hardcover ISBN: 978-1-4020-6355-8Published: 26 July 2007
Softcover ISBN: 978-94-007-9702-4Published: 30 October 2014
eBook ISBN: 978-1-4020-6356-5Published: 06 November 2007
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: XIX, 399
Additional Information: Jointly published with Canopus Publishing Limited, Bristol, UK
Topics: Complex Systems, Dynamical Systems and Ergodic Theory, Applied and Technical Physics, Applications of Mathematics, Mathematical and Computational Engineering, Engineering, general