Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model

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

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We analyse pinned front and pulse solutions in a singularly perturbed three-component FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit conditions for the existence and stability of these type of pinned solutions by combining geometric singular perturbation techniques and an action functional approach. Most notably, in certain parameter regimes we can explicitly compute the pinning distance of a localised solution to the defect.

Original languageEnglish
Pages (from-to)153-203
Number of pages51
JournalJournal of Dynamics and Differential Equations
Volume31
Issue number1
DOIs
Publication statusPublished - 2019 Mar 15

Keywords

  • Calculus of variations
  • Defects
  • Existence
  • Localised defect solutions
  • Reaction–diffusion equations
  • Singular perturbations
  • Stability

ASJC Scopus subject areas

  • Analysis

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