Nucleation of waves in excitable media by noise

Shardlow, Tony (2004) Nucleation of waves in excitable media by noise. Multiscale Modeling and Simulation, 3 (1). pp. 151-167. ISSN 1540-3459

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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.

Item Type: Article
Uncontrolled Keywords: reaction-diffusion equations, stochastic PDEs, excitable media
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 14 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/479

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