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Kelkel, Jan; Surulescu, Christina

On a stochastic reaction-diffusion system modeling pattern formation on seashells. (English) Zbl 1198.92004

J. Math. Biol. 60, No. 6, 765-796 (2010).
Summary: Starting from an A. Gierer and H. Meinhardt setting [see Math. Quest. Biol. 6, Proc 8th Symp. Math. Biol., San Francisco 1974, 163–183 (1974; Zbl 0297.92007)], we propose a stochastic model to characterize pattern formation on seashells under the influence of random space-time fluctuations. We prove the existence of a positive solution for the resulting system and perform numerical simulations in order to assess the behavior of the solution in comparison with a deterministic approach.

Cited in 10 Documents

MSC:

92C15 Developmental biology, pattern formation
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K57 Reaction-diffusion equations

Keywords:

Pattern formation; Stochastic reaction-diffusion equations

Citations:

Zbl 0297.92007
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\textit{J. Kelkel} and \textit{C. Surulescu}, J. Math. Biol. 60, No. 6, 765--796 (2010; Zbl 1198.92004)
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References:

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