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Numerical continuation methods for large-scale dissipative dynamical systems

A tutorial on continuation and bifurcation methods for the analysis of truncated dissipative partial differential equations is presented. It focuses on the computation of equilibria, periodic orbits, their loci of codimension-one bifurcations, and invariant tori. To make it more self-contained, it i...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2016-11, Vol.225 (13-14), p.2465-2486
Main Authors: Umbría, Juan Sánchez, Net, Marta
Format: Article
Language:English
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Summary:A tutorial on continuation and bifurcation methods for the analysis of truncated dissipative partial differential equations is presented. It focuses on the computation of equilibria, periodic orbits, their loci of codimension-one bifurcations, and invariant tori. To make it more self-contained, it includes some definitions of basic concepts of dynamical systems, and some preliminaries on the general underlying techniques used to solve non-linear systems of equations by inexact Newton methods, and eigenvalue problems by means of subspace or Arnoldi iterations.
ISSN:1951-6355
1951-6401
1951-6401
DOI:10.1140/epjst/e2015-50317-2