Numerical continuation methods for dynamical systems : path following and boundary value problems
Author(s)
Bibliographic Information
Numerical continuation methods for dynamical systems : path following and boundary value problems
(Understanding complex systems / founding editor, J.A. Scott Kelso)(Springer complexity)
Springer , Canopus publishing, c2007
- : pbk
Available at 8 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Dedicated to Eusebius J. Doedel for his 60th birthday"
Description and Table of Contents
Description
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.
Table of Contents
- Introduction Foreword
- Herbert B. Keller. 1. Lecture Notes on Numerical Analysis of Nonlinear Equations
- Eusebius J. Doedel. 2. Interactive Continuation Tools
- Willy Govaerts and Yuri A. Kuznetzov. 3. Higher-Dimensional Continuation
- Michael E. Henderson. 4. Computing Invariant Manifolds via the Continuation of Orbit Segments
- Bernd Krauskopf and Hinke M. Osinga. 5. The Dynamics of SQUIDs and Coupled Pendula
- Donald G. Aronson and Hans G. Othmer. 6. Global Bifurcation Analysis in Laser Systems
- Emilio Freire and Alejandro J. Rodriguez-Luis. 8. Periodic Orbit Continuation in Multiple Time Scale Systems
- John Guckenheimer and M. Drew Lamar. 9. Continuation of Periodic orbits in Symmetric Hamiltonian Systems
- Jorge Galan-Vioque aand Andre Vanderbauwhede. 10. Phase Conditions, Symmetries and PDE Continuation
- Wolf-Jurgen Beyn and Vera Thummler. 11. Numerical Computation of Coherent Structures
- Alan R. Champneys and Bjoern Sandstede. 12. Continuation and Bifurcation Analysis of Delay Differential Equations
- Dirk Roose and Robert Szalai. Index.
by "Nielsen BookData"