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This article is cited in 5 scientific papers (total in 5 papers)
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.
Received: 01.04.2019
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
Linking options:
https://www.mathnet.ru/eng/iimi372 https://www.mathnet.ru/eng/iimi/v53/p73
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Abstract page: | 298 | Full-text PDF : | 211 | References: | 29 |
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