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 journalArticlepeer-review

12 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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