PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM.

John Rinzel, David Terman

Research output: Contribution to journalArticle

Abstract

Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

Original languageEnglish (US)
Pages (from-to)1111-1137
Number of pages27
JournalSIAM Journal on Applied Mathematics
Volume42
Issue number5
StatePublished - Oct 1982

Fingerprint

Bistable System
Reaction-diffusion System
Propagation
FitzHugh-Nagumo
Singular Perturbation
Nerve
Reaction-diffusion Equations
Singular Point
Conduction
Piecewise Linear
Traveling Wave
Vary
Nonlinearity
Numerical Results
Range of data

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM. / Rinzel, John; Terman, David.

In: SIAM Journal on Applied Mathematics, Vol. 42, No. 5, 10.1982, p. 1111-1137.

Research output: Contribution to journalArticle

@article{32eea3a8f23b4a43b2d9618626aff12a,
title = "PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM.",
abstract = "Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.",
author = "John Rinzel and David Terman",
year = "1982",
month = "10",
language = "English (US)",
volume = "42",
pages = "1111--1137",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",

}

TY - JOUR

T1 - PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM.

AU - Rinzel, John

AU - Terman, David

PY - 1982/10

Y1 - 1982/10

N2 - Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

AB - Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

UR - http://www.scopus.com/inward/record.url?scp=0020191444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020191444&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0020191444

VL - 42

SP - 1111

EP - 1137

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -