Singular perturbation theory of traveling waves in excitable media (A review)
type: Item
instance of: scholarly article
title: Singular perturbation theory of traveling waves in excitable media (A review)
zbMATH Open document ID: 0656.76018
DOI: 10.1016/0167-2789(88)90062-0
author: John J. Tyson
author: James P. Keener
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: Waves of chemical or electrical activity, traveling through space, have been observed in several contexts: chemical reaction mixtures in non- convecting liquid phase, cell-suspensions, nerve axons, and neuromuscular tissues. Typically, wave-supporting preparations are excitable; that is, they respond sensitively to perturbations: small perturbations are rapidly damped out, but suprathreshold disturbances trigger an abrupt and substantial response. The abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media. Singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious, but the analysis of periodic nonlinear waves in excitable two-dimensional media has been carried out in several fundamentally different ways. Our intention is to bring some order to the important but difficult theory of propagating waves in two-dimensional excitable media. In conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three-dimensional space.
Mathematics Subject Classification ID: 76B99
Mathematics Subject Classification ID: 76-02
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 74J99
zbMATH DE Number: 4072564
zbMATH Keywords: chemical reaction mixtures
zbMATH Keywords: non-convecting liquid phase
zbMATH Keywords: cell- suspensions
zbMATH Keywords: nerve axons
zbMATH Keywords: neuromuscular tissues
zbMATH Keywords: methods of singular perturbation theory
MaRDI profile type: Publication
full work available at URL: 0167-2789(88)90062-0
OpenAlex ID: W2060809971
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description: scientific article; zbMATH DE number 4072564