Numerical Continuation Methods for Dynamical Systems
Publication year: 2007
ISBN: 978-1-4020-6356-5
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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.
Subject: Mathematics and Statistics, 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
