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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 3, Pages 430–449
DOI: https://doi.org/10.7868/S0044466914030065 (Mi zvmmf10005) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On a modification of the FitzHugh–Nagumo neuron model

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

a Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia
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DOI: https://doi.org/10.7868/S0044466914030065
Abstract: A singularly perturbed system of ordinary differential equations with a fast and a slow variable is proposed, which is a modification of the well-known FitzHugh–Nagumo model from neuroscience. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a $\delta$-like function.
Key words: FitzHugh–Nagumo neuron model, relaxation cycle, asymptotics, stability, buffer phenomenon.
Received: 14.10.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 3, Pages 443–461
DOI: https://doi.org/10.1134/S0965542514030063
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “On a modification of the FitzHugh–Nagumo neuron model”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 430–449; Comput. Math. Math. Phys., 54:3 (2014), 443–461
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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