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Numerical Continuation Methods for Dynamical Systems - Path following and boundary value problems (Paperback, 2007 ed.)
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Numerical Continuation Methods for Dynamical Systems - Path following and boundary value problems (Paperback, 2007 ed.)
Series: Understanding Complex Systems
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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.
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