Pattern formation in small arrays of locally coupled oscillators

Rebecca Ellison, Virginia Gardner, Joel Lepak, Meghan O'Malley, Joseph Paullet, Joseph Previte, Beth Ann Reid, Katy Vizzard

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We investigate small two-dimensional arrays of locally coupled phase oscillators which are shown to exhibit a surprising variety of stable structures which include: single spiral waves, spiral pairs and spirals with secondary periodic core motion. This periodic core motion is not the core meander familiar to many models of active media, but is in fact induced by the boundary of the small domain. Such boundary motion was investigated by Sepulchre and Babloyantz [1993] for the complex Ginzburg-Landau equation and for the Brusselator model in a relaxation oscillation parameter regime. The current model confirms the findings in [Sepulchre & Babloyantz, 1993] and sheds new light on the origin of such motion. The model also exhibits other patterns, as well as a chaotic regime. We discuss the transition between patterns as the form of the coupling is changed as well as implications for pattern formation in general oscillatory media.

Original languageEnglish (US)
Pages (from-to)2283-2293
Number of pages11
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume15
Issue number7
DOIs
StatePublished - Jul 2005

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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