Izv. IMI UdGU, 2019, Volume 53, Pages 73–82
This article is cited in 1 scientific paper (total in 1 paper)
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
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.
reaction-diffusion model, Turing instability, self-organization, pattern formation, noise-induced dynamics, modality analysis.
|Russian Science Foundation
|This research was supported by the Russian Science Foundation (project no. 16-11-10098).
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MSC: 70K50, 65C30, 60H30
A. P. Kolinichenko, L. B. Ryashko, “Modality analysis of patterns in reaction-diffusion systems with random perturbations”, Izv. IMI UdGU, 53 (2019), 73–82
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\by A.~P.~Kolinichenko, L.~B.~Ryashko
\paper Modality analysis of patterns in reaction-diffusion systems with random perturbations
\jour Izv. IMI UdGU
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This publication is cited in the following articles:
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
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