Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
type: Item
instance of: scholarly article
title: Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
zbMATH Open document ID: 1402.35026
author: P. van Heijster
author: Chao-Nien Chen
author: Yasumasa Nishiura
author: Takashi Teramoto
published in: Journal of Dynamics and Differential Equations
publication date: 2018-08-21T00:00:00Z
review text: The authors introduce a variational approach to revisit the study of stationary pulse solutions of a singularly perturbed FitzHugh-Nagumo system. They find some action function whose (minimizers) critical points are (stable) stationary solutions. This allows them to formally recover earlier results from the literature while avoiding most of the technical machinery (Evans function and nonlocal eigenvalue problem approaches), and to formulate new conjectures on the stability of various types of pulses (asymmetric or with several peaks).
reviewed by: Thomas Giletti
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 6921338
zbMATH Keywords: activator-inhibitor model
zbMATH Keywords: pulse solutions
zbMATH Keywords: variational approach
MaRDI profile type: Publication
full work available at URL: s10884-016-9557-z
OpenAlex ID: W2533252060
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DOI: 10.1007/S10884-016-9557-Z
description: scientific article; zbMATH DE number 6921338