Attraction basin of the equilibrium configuration in the FitzHugh-Nagumo model
type: Item
instance of: scholarly article
title: Attraction basin of the equilibrium configuration in the FitzHugh-Nagumo model
zbMATH Open document ID: 1269.34052
author: Chiara Lelli
published in: Acta Applicandae Mathematicae
publication date: 2013-01-02T00:00:00Z
review text: Consider the FitzHugh-Nagumo model \[ \begin{aligned} \varepsilon{dv\over dt} &= v(1-v)(v-\alpha)- w,\\ {dw\over dt} &= v-\gamma w.\end{aligned}\tag{\(*\)} \] The author derives conditions on the coefficients \(\alpha\), \(\gamma\), \(\varepsilon\) such that \((*)\) has no limit cycle. The proof is based on the transformation of \((*)\) into a Liénard sytem of the type \[ \begin{aligned} {dx\over dt} &= y- F(x),\\ {dy\over dt} &= -g(x)\end{aligned}\tag{\(**\)} \] and on the application of a criterion due to \textit{J. Sugie} [Q. Appl. Math. 49, No. 3, 543--554 (1991; Zbl 0736.34043)] on the nonexistence of a limit cycle of system \((**)\).
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 6121145
zbMATH Keywords: FitzHugh-Nagumo system
zbMATH Keywords: spike solutions
zbMATH Keywords: limit cycles
zbMATH Keywords: bounded orbits
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: s10440-012-9744-9
OpenAlex ID: W2082959767
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DOI: 10.1007/S10440-012-9744-9
description: scientific article; zbMATH DE number 6121145