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Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems: Understanding Complex Systems

Editat de Bernd Krauskopf, Hinke M. Osinga, Jorge Galan-Vioque
en Limba Engleză Hardback – 26 iul 2007
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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Specificații

ISBN-13: 9781402063558
ISBN-10: 1402063555
Pagini: 400
Ilustrații: XIX, 399 p.
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.75 kg
Ediția:2007
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Understanding Complex Systems

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

Lecture Notes on Numerical Analysis of Nonlinear Equations.- Interactive Continuation Tools.- Higher-Dimensional Continuation.- Computing Invariant Manifolds via the Continuation of Orbit Segments.- The Dynamics of SQUIDs and Coupled Pendula.- Global Bifurcation Analysis in Laser Systems.- Numerical Bifurcation Analysis of Electronic Circuits.- Periodic Orbit Continuation in Multiple Time Scale Systems.- Continuation of Periodic Orbits in Symmetric Hamiltonian Systems.- Phase Conditions, Symmetries and PDE Continuation.- Numerical Computation of Coherent Structures.- Continuation and Bifurcation Analysis of Delay Differential Equations.

Textul de pe ultima copertă

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.

Caracteristici

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