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.
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
\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}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000487290700007}
\elib{https://elibrary.ru/item.asp?id=38503200}
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https://www.mathnet.ru/eng/iimi372
https://www.mathnet.ru/eng/iimi/v53/p73
This publication is cited in the following 5 articles:
Irina Bashkirtseva, Anna Stepanova, Ivan Tsvetkov, THE VIII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2021), 2466, THE VIII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2021), 2022, 090028
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
Alexander Pankratov, Irina Bashkirtseva, THE VII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2020), 2313, THE VII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2020), 2020, 080023
A. P. Kolinichenko, L. B. Ryashko, THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019, 2314, THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019, 2020, 080017
Irina Bashkirtseva, Svetlana Zaitseva, THE VII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2020), 2313, THE VII INTERNATIONAL YOUNG RESEARCHERS' CONFERENCE – PHYSICS, TECHNOLOGY, INNOVATIONS (PTI-2020), 2020, 080001
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