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Matematicheskoe modelirovanie, 2020, Volume 32, Number 6, Pages 53–65
DOI: https://doi.org/10.20948/mm-2020-06-04 (Mi mm4188) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Pattern formation in reaction-diffusion system with time-fractional derivatives

D. A. Zenyuk, G. G. Malinetsky

Keldysh Institute of Applied Mathematics, Russian Academy of Science, Moscow
Full-text PDF (566 kB) Citations (2)
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DOI: https://doi.org/10.20948/mm-2020-06-04
Abstract: In the present paper possible scenarios of pattern formation in non-linear media with diffusion and differential operators of non-integer order are studied for the abstract Brusselator model. By means of the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that stability criteria significantly depend on the order of the fractional derivative in case of the Hopf and C2TH bifurcations. Predictions of the linear theory are confirmed by numerical simulation.
Keywords: fractional calculus, reaction-diffusion systems.
Received: 28.10.2019
Revised: 28.10.2019
Accepted: 23.12.2019
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 1, Pages 126–133
DOI: https://doi.org/10.1134/S2070048221010178
Document Type: Article
Language: Russian
Citation: D. A. Zenyuk, G. G. Malinetsky, “Pattern formation in reaction-diffusion system with time-fractional derivatives”, Mat. Model., 32:6 (2020), 53–65; Math. Models Comput. Simul., 13:1 (2021), 126–133
Citation in format AMSBIB
\Bibitem{ZenMal20}
\by D.~A.~Zenyuk, G.~G.~Malinetsky
\paper Pattern formation in reaction-diffusion system with time-fractional derivatives
\jour Mat. Model.
\yr 2020
\vol 32
\issue 6
\pages 53--65
\mathnet{http://mi.mathnet.ru/mm4188}
\crossref{https://doi.org/10.20948/mm-2020-06-04}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 1
\pages 126--133
\crossref{https://doi.org/10.1134/S2070048221010178}
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  • https://www.mathnet.ru/eng/mm4188
  • https://www.mathnet.ru/eng/mm/v32/i6/p53
    • This publication is cited in the following 2 articles:
    1. D. A. Zenyuk, G. G. Malinetsky, “Linear stability analysis for reaction–subdiffusion system of mixed order”, Math. Models Comput. Simul., 14:3 (2022), 381–388  mathnet  crossref  crossref
    2. D. A. Zenyuk, G. G. Malinetskiy, “Pattern formation mechanisms in one-dimensional Brusselator with fractional derivatives”, Keldysh Institute preprints, 2020, 85–24  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    Full-text PDF :109
    References:48
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