Stable rotating waves in two-dimensional discrete active media

Joseph E. Paullet, G. Bard Ermentrout

Research output: Contribution to journalArticle

48 Scopus citations

Abstract

The existence and stability of stable rotating solutions (spiral waves) in a discrete system of coupled phase models is proven. Monotone methods are used to obtain existence and qualitative features of the solutions. An application of Fenichel's results for singular perturbation implies the existence for a one variable model for excitability. Numerical comparisons with the phase model and a realistic membrane model are made. A numerically computed Hopf bifurcation shows the existence of the `wobbling core' observed in spatially continuous models.

Original languageEnglish (US)
Pages (from-to)1720-1744
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume54
Issue number6
DOIs
StatePublished - Jan 1 1994

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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