Homoclinic branch switching: A numerical implementation of Lin's method

BE Oldeman, AR Champneys, B Krauskopf

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)
223 Downloads (Pure)

Abstract

We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N-homoclinic orbit, for any N>1 (if it exists nearby). This scheme is based on Lin's method and it is robust and reliable.

The method is implemented in AUTO/HOMCONT. A system of ordinary differential equations introduced by Sandstede featuring inclination and orbit flip bifurcations and homoclinic-doubling cascades, is used as a test bed for the algorithm. It is also successfully applied to reliably find multihump traveling wave solutions in the FitzHugh–Nagumo nerve-axon equations and in a fourth-order Hamiltonian system arising as a model for water waves.
Translated title of the contributionHomoclinic branch switching: A numerical implementation of Lin's method
Original languageEnglish
Pages (from-to)2977-2999
Number of pages23
JournalInternational Journal of Bifurcation and Chaos
Volume13
Issue number10
DOIs
Publication statusPublished - 2003

Keywords

  • Homoclinic bifurcations
  • numerical continuation
  • branch switching

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