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Izv. IMI UdGU, 2020, Volume 55, Pages 155–163 (Mi iimi396)  

MATHEMATICS

Analysis of stochastic sensitivity of Turing patterns in distributed reaction–diffusion systems

A. P. Kolinichenko, L. B. Ryashko

Ural Federal University, ul. Lenina, 51, Yekaterinburg, 620075, Russia

Abstract: In this paper, a distributed stochastic Brusselator model with diffusion is studied. We show that a variety of stable spatially heterogeneous patterns is generated in the Turing instability zone. The effect of random noise on the stochastic dynamics near these patterns is analysed by direct numerical simulation. Noise-induced transitions between coexisting patterns are studied. A stochastic sensitivity of the pattern is quantified as the mean-square deviation from the initial unforced pattern. We show that the stochastic sensitivity is spatially non-homogeneous and significantly differs for coexisting patterns. A dependence of the stochastic sensitivity on the variation of diffusion coefficients and intensity of noise is discussed.

Keywords: reaction–diffusion model, Turing instability, self-organization, stochastic sensitivity

Funding Agency Grant Number
Russian Science Foundation 16--11--10098
The study was funded by Russian Science Foundation, project number 16–11–10098.


DOI: https://doi.org/10.35634/2226-3594-2020-55-10

Full text: PDF file (1451 kB)
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Bibliographic databases:

UDC: 517.958, 544.431.8
MSC: 70K50, 65C30, 60H30
Received: 15.03.2020
Language:

Citation: A. P. Kolinichenko, L. B. Ryashko, “Analysis of stochastic sensitivity of Turing patterns in distributed reaction–diffusion systems”, Izv. IMI UdGU, 55 (2020), 155–163

Citation in format AMSBIB
\Bibitem{KolRya20}
\by A.~P.~Kolinichenko, L.~B.~Ryashko
\paper Analysis of stochastic sensitivity of Turing patterns
in~distributed reaction--diffusion systems
\jour Izv. IMI UdGU
\yr 2020
\vol 55
\pages 155--163
\mathnet{http://mi.mathnet.ru/iimi396}
\crossref{https://doi.org/10.35634/2226-3594-2020-55-10}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000547994700010}


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