QUASI-PERIODIC WAVES ALONG A PULSATING PROPAGATING FRONT IN A REACTION-DIFFUSION SYSTEM.

T. Erneux*, B. J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

The authors consider a system of reaction-diffusion equations for which there exists a solution with a uniformly propagating front, and from which solutions describing a pulsating propagating front with periodic traveling and standing waves along the front, bifurcate supercritically. They construct a pulsating propagating solution branch, with quasi-periodic traveling waves along its front, which connects the periodic traveling and standing wave branches. Thus the quasi-periodic branch arises as a secondary bifurcation from the uniformly propagating solution. Their construction involves a perturbation analysis in the neighborhood of a certain degenerate point in parameter space. The stability of the various solution branches is investigated.

Original languageEnglish (US)
Pages (from-to)536-544
Number of pages9
JournalSIAM Journal on Applied Mathematics
Volume44
Issue number3
DOIs
StatePublished - Jan 1 1984

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ASJC Scopus subject areas

  • Applied Mathematics

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