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Numerical continuation methods for large-scale dissipative dynamical systems

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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.

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Authors and Affiliations

  1. Departament de Física, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

    Juan Sánchez Umbría & Marta Net

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  1. Juan Sánchez Umbría
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  2. Marta Net
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Correspondence to Juan Sánchez Umbría or Marta Net.

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Umbría, J.S., Net, M. Numerical continuation methods for large-scale dissipative dynamical systems. Eur. Phys. J. Spec. Top. 225, 2465–2486 (2016). https://doi.org/10.1140/epjst/e2015-50317-2

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  • DOI: https://doi.org/10.1140/epjst/e2015-50317-2

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