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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 1, Pages 94–110
DOI: https://doi.org/10.7868/S0044466917010070 (Mi zvmmf10510) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Two-frequency self-oscillations in a FitzHugh–Nagumo neural network

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

a Faculty of Mathematics, Yaroslavl State University, Yaroslavl, Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.7868/S0044466917010070
Abstract: A new mathematical model of a one-dimensional array of FitzHugh–Nagumo neurons with resistive-inductive coupling between neighboring elements is proposed. The model relies on a chain of diffusively coupled three-dimensional systems of ordinary differential equations. It is shown that any finite number of coexisting stable invariant two-dimensional tori can be obtained in this chain by suitably increasing the number of its elements.
Key words: FitzHugh–Nagumo neural network, normal form, invariant torus, asymptotic behavior, stability, buffer phenomenon.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-04066_a
Ministry of Education and Science of the Russian Federation 2014/258-1875
Received: 26.01.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 1, Pages 106–121
DOI: https://doi.org/10.1134/S0965542517010067
Bibliographic databases:
Document Type: Article
UDC: 519.924.2
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Two-frequency self-oscillations in a FitzHugh–Nagumo neural network”, Zh. Vychisl. Mat. Mat. Fiz., 57:1 (2017), 94–110; Comput. Math. Math. Phys., 57:1 (2017), 106–121
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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