A mechanism for switching near a heteroclinic network

Vivien Kirk, Emily Lane, Claire M. Postlethwaite, Alastair M. Rucklidge, Mary Silber

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We describe an example of a robust heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling due to complex eigenvalues in the flow linearized about one of the equilibria common to all cycles in the network. We construct and use return maps to investigate the asymptotic stability of the network, and show that switching is ubiquitous near the network. Some of the unstable manifolds involved in the network are two-dimensional; we develop a technique to account for all trajectories on those manifolds. A simple numerical example illustrates the rich dynamics that can result from the interplay between the various cycles in the network.

Original languageEnglish (US)
Pages (from-to)323-349
Number of pages27
JournalDynamical Systems
Volume25
Issue number3
DOIs
StatePublished - Sep 1 2010

Keywords

  • heteroclinic cycle
  • heteroclinic network
  • switching

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

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