Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

Peter Van Heijster*, Björn Sandstede

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

Abstract

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, centre-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Original languageEnglish
Pages (from-to)19-34
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Volume275
DOIs
Publication statusPublished - 1 May 2014
Externally publishedYes

Keywords

  • Bifurcations
  • FitzHugh-Nagumo system
  • Planar localized structures
  • Travelling spots

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