Existence of spiral waves in an oscillatory reaction-diffusion system

Joseph E. Paullet, Bard Ermentrout, William Troy

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Abstract

Rotating waves are proven to exist on the unit disk for an oscillatory reaction-diffusion equation with Neuman boundary conditions. The method of proof relies on a two-parameter shooting argument for the ensemble frequency and the radial derivative of the magnitude. Numerical solutions indicate that the waves are stable if the diffusion is sufficiently small. It is also shown that these solutions cease to exist for large diffusion. The origin of the rotating waves is discussed.

Original languageEnglish (US)
Pages (from-to)1386-1401
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume54
Issue number5
DOIs
Publication statusPublished - Jan 1 1994

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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