Nucleation of waves in excitable media by noise

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Abstract

We are interested in reaction-diffusion equations that model excitable media under the influence of an additive noise. In many models of this type, the homogeneous zero state is stable, and interesting dynamics are observed only for certain initial data. In the presence of noise, the excitable media is stimulated, and the noise may be sufficiently large to nucleate wave forms. In computations, we see for small noise that only target waves are nucleated when the time scales for excitation and inhibition are sufficiently separated. We provide a theorem that supports this observation.
Original languageEnglish
Pages (from-to)151-167
Number of pages17
JournalMultiscale Modeling and Simulation : A SIAM Interdisciplinary Journal
Volume3
Issue number1
DOIs
Publication statusPublished - 31 Dec 2004

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