Planar radial spots in a three-component FitzHugh-Nagumo system

Peter Van Heijster*, Björn Sandstede

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

27 Citations (Scopus)

Abstract

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

Original languageEnglish
Pages (from-to)705-745
Number of pages41
JournalJournal of Nonlinear Science
Volume21
Issue number5
DOIs
Publication statusPublished - Oct 2011
Externally publishedYes

Keywords

  • FitzHugh-Nagumo system
  • Geometrical singular perturbation theory
  • Planar localized structures
  • Stability analysis

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