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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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Published in: | The European physical journal. ST, Special topics Special topics, 2016-11, Vol.225 (13-14), p.2465-2486 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 1951-6355 1951-6401 1951-6401 |
DOI: | 10.1140/epjst/e2015-50317-2 |