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
DOIs
StatePublished - Jan 1 1982

ASJC Scopus subject areas

  • Applied Mathematics

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