The European Physical Journal Special Topics

, Volume 225, Issue 13, pp 2465–2486

Numerical continuation methods for large-scale dissipative dynamical systems

Review Review articles

DOI: 10.1140/epjst/e2015-50317-2

Cite this article as:
Umbría, J.S. & Net, M. Eur. Phys. J. Spec. Top. (2016) 225: 2465. doi:10.1140/epjst/e2015-50317-2
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Part of the following topical collections:
  1. Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental Approaches

Abstract

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.

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Departament de Física, Universitat Politècnica de CatalunyaBarcelonaSpain

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