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Izv. IMI UdGU, 2019, Volume 53, Pages 73–82 (Mi iimi372)  

Modality analysis of patterns in reaction-diffusion systems with random perturbations

A. P. Kolinichenko, L. B. Ryashko

Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Lenina, 51, Yekaterinburg, 620075, Russia

Abstract: In this paper, a distributed Brusselator model with diffusion is investigated. It is well known that this model undergoes both Andronov–Hopf and Turing bifurcations. It is shown that in the parametric zone of diffusion instability the model generates a variety of stable spatially nonhomogeneous structures (patterns). This system exhibits a phenomenon of the multistability with the diversity of stable spatial structures. At the same time, each pattern has its unique parametric range, on which it may be observed. The focus is on analysis of stochastic phenomena of pattern formation and transitions induced by small random perturbations. Stochastic effects are studied by the spatial modality analysis. It is shown that the structures possess different degrees of stochastic sensitivity.

Keywords: reaction-diffusion model, Turing instability, self-organization, pattern formation, noise-induced dynamics, modality analysis.

Funding Agency Grant Number
Russian Science Foundation 16-11-10098
This research was supported by the Russian Science Foundation (project no. 16-11-10098).


DOI: https://doi.org/10.20537/2226-3594-2019-53-07

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UDC: 517.958, 544.431.8
MSC: 70K50, 65C30, 60H30
Received: 01.04.2019
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Citation: A. P. Kolinichenko, L. B. Ryashko, “Modality analysis of patterns in reaction-diffusion systems with random perturbations”, Izv. IMI UdGU, 53 (2019), 73–82

Citation in format AMSBIB
\Bibitem{KolRya19}
\by A.~P.~Kolinichenko, L.~B.~Ryashko
\paper Modality analysis of patterns in reaction-diffusion systems with random perturbations
\jour Izv. IMI UdGU
\yr 2019
\vol 53
\pages 73--82
\mathnet{http://mi.mathnet.ru/iimi372}
\crossref{https://doi.org/10.20537/2226-3594-2019-53-07}
\elib{http://elibrary.ru/item.asp?id=38503200}


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