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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 9, Pages 1495–1515
DOI: https://doi.org/10.1134/S0044466919090096 (Mi zvmmf10949) 		 
Autowave processes in diffusion neuron systems

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a Faculty of Mathematics, Yaroslavl State University, Yaroslavl, 150000 Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
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DOI: https://doi.org/10.1134/S0044466919090096
Abstract: A diffusion neuron model representing a system of $m$, $m\geqslant 2$, identical nonlinear delay differential equations coupled by linear diffusion terms is considered. It is shown that, with a suitable choice of the diffusion coefficient, the system has a set of $m$ stable relaxation cycles.
Key words: bilocal model, autowave processes, asymptotic behavior, stability, diffusion system.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10055_мк
This work was supported by the Russian Foundation for Basic Research, project no. 18-29-10055.
Received: 25.04.2019
Revised: 25.04.2019
Accepted: 15.05.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 9, Pages 1434–1453
DOI: https://doi.org/10.1134/S0965542519090094
Bibliographic databases:
Document Type: Article
UDC: 519.926
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Autowave processes in diffusion neuron systems”, Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019), 1495–1515; Comput. Math. Math. Phys., 59:9 (2019), 1434–1453
Citation in format AMSBIB
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