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Numerical Continuation Methods for Dynamical Systems

Path following and boundary value problems

  • Bernd Krauskopf
  • Hinke M. Osinga
  • Jorge Galán-Vioque

Table of contents

  1. Front Matter
    Pages i-xix
  2. Willy Govaerts, Yuri A Kuznetsov
    Pages 51-75
  3. Michael E Henderson
    Pages 77-115
  4. Bernd Krauskopf, Hinke M. Osinga
    Pages 117-154
  5. Donald G Aronson, Hans G Othmer
    Pages 155-176
  6. Sebastian M Wieczorek
    Pages 177-220
  7. Emilio Freire, Alejandro J Rodríguez-Luis
    Pages 221-251
  8. John Guckenheimer, M Drew LaMar
    Pages 253-267
  9. Jorge Galán-Vioque, André Vanderbauwhede
    Pages 269-299
  10. Wolf-Jürgen Beyn, Vera Thümmler
    Pages 301-330
  11. Alan R Champneys, Björn Sandstede
    Pages 331-358

About this book

Introduction

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.

Keywords

Canopus PDE continuation SQUIDs and coupled pendula bifurcation analysis calculus delay differential equations differential equation dynamical systems invariant manifolds numerical analysis partial differential equation periodic orbits systems theory

Editors and affiliations

  • Bernd Krauskopf
    • 1
  • Hinke M. Osinga
    • 1
  • Jorge Galán-Vioque
    • 2
  1. 1.Dept of Engineering MathematicsUniversity of BristolUK
  2. 2.University of Sevilla Escuela Superior de IngenierosSpain

Bibliographic information