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

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.


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


Zbl 0297.92007
Full Text: DOI


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