New modes of quasi-periodic combustion near a degenerate Hopf bifurcation point

Stephen B. Margolis*, Bernard J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

Steady, planar propagation of a condensed phase reaction front is unstable to disturbances corresponding to pulsating and spinning waves for sufficiently large values of a parameter related to the activation energy. This paper considers the nonlinear evolution equations for the amplitudes of the pulsating and spinning waves in a neighborhood of a double eigenvalue of the problem linearized about the steady, planar solution. In particular, near a degenerate Hopf bifurcation point, closed branches of solutions which represent new quasi-periodic modes of combustion are described.

Original languageEnglish (US)
Pages (from-to)828-853
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume48
Issue number4
DOIs
StatePublished - Jan 1 1988

ASJC Scopus subject areas

  • Applied Mathematics

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