Butterfly catastrophe for fronts in a three-component reaction-diffusion system
type: Item
instance of: scholarly article
title: Butterfly catastrophe for fronts in a three-component reaction-diffusion system
zbMATH Open document ID: 1325.35088
author: Martina Chirilus-Bruckner
author: Arjen Doelman
author: P. van Heijster
author: Jens D. M. Rademacher
published in: Journal of Nonlinear Science
publication date: 2015-03-25T00:00:00Z
review text: The subject of the paper is the analysis of bifurcations of solutions for propagating fronts in a three-component one-dimensional reaction-diffusion model of the FitzHugh-Nagumo type, where single- and multiple-front patterns are basic dynamical states. The application of a combination of various analytical methods, such as singular perturbation theory, center-manifold reduction, and Evans function, reveals a rather complex picture of bifurcations. These results suggest an explanation to numerically observed dynamical regimes in the form of accelerating and oscillating fronts. The most essential peculiarity of the analysis is that it focuses on the case when the essential spectrum of perturbations around the underlying front solution is asymptotically close to the imaginary axis.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B36
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 6419572
zbMATH Keywords: FitzHugh-Nagumo model
zbMATH Keywords: singular perturbation theory
zbMATH Keywords: center-manifold reduction
zbMATH Keywords: Evans function
MaRDI profile type: Publication
full work available at URL: s00332-014-9222-9
OpenAlex ID: W2085170514
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DOI: 10.1007/S00332-014-9222-9
description: scientific article; zbMATH DE number 6419572