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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2019 Volume 59, Number 9, Pages 1495–1515 (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

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.

UDC: 519.926

Received: 25.04.2019
Revised: 25.04.2019
Accepted: 15.05.2019

DOI: 10.1134/S0044466919090096


 English version:
Computational Mathematics and Mathematical Physics, 2019, 59:9, 1434–1453

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© Steklov Math. Inst. of RAS, 2024