Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model
type: Item
instance of: scholarly article
title: Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model
zbMATH Open document ID: 1415.35018
author: P. van Heijster
author: Chao-Nien Chen
author: Yasumasa Nishiura
author: Takashi Teramoto
published in: Journal of Dynamics and Differential Equations
publication date: 2019-04-25T00:00:00Z
review text: This article presents an analysis of a singularly perturbed three-component FitzHugh-Nagumo model with a small jump-type heterogeneity. The authors consider pinned front solutions and pulse solutions for the model problem. Explicit conditions for the existence and stability of the pinned front solutions are demonstrated. For this, geometric singular perturbation techniques with an action functional approach are employed (the interested reader should also see [\textit{A. Doelman} et al., SIAM J. Appl. Dyn. Syst. 15, No. 2, 655--712 (2016; Zbl 1343.34041)]). One novelty in this article is the determination of particular parameter ranges where one can explicitly compute the pinning distance of a local defect solution. It should also be mentioned that local defect solutions were investigated numerically in [\textit{P. van Heijster} et al., Nonlinearity 24, No. 1, 127--157 (2011; Zbl 1208.35010)].
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 7047663
zbMATH Keywords: localised defect solutions
zbMATH Keywords: small jump-type heterogeneity
zbMATH Keywords: pinned front solutions
zbMATH Keywords: pulse solutions
zbMATH Keywords: pinning distance
reviewed by: Joseph Shomberg
MaRDI profile type: Publication
full work available at URL: s10884-018-9694-7
OpenAlex ID: W2887850585
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Wikidata QID: Q129405014
DOI: 10.1007/S10884-018-9694-7