Localized Patterns in a Three-Component FitzHugh–Nagumo Model Revisited Via an Action Functional

Peter van Heijster, Chao Nien Chen, Yasumasa Nishiura, Takashi Teramoto

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this manuscript, we combine geometrical singular perturbation techniques and an action functional to revisit—and further study—the existence and stability of stationary localized structures in a singularly perturbed three-component FitzHugh–Nagumo model. In particular, the action functional replaces the Melnikov integral approach used in Doelman et al. (J Dyn Differ Equ 21:73–115, 2009) to explicitly derive existence conditions for stationary localized structures. In addition, the action functional also gives critical information on the stability of these stationary localized structures, thus circumventing a tedious Evans function computation. This highlights the strength of the action functional approach.

Original languageEnglish
Pages (from-to)521-555
Number of pages35
JournalJournal of Dynamics and Differential Equations
Volume30
Issue number2
DOIs
Publication statusPublished - 2018 Jun 1

Keywords

  • Activator–inhibitor model
  • Calculus of variations
  • Existence
  • Reaction–diffusion system
  • Singular perturbations
  • Stability

ASJC Scopus subject areas

  • Analysis

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