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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 5, Pages 840–858 (Mi zvmmf9713)  
This article is cited in 26 scientific papers (total in 26 papers)

Discrete autowaves in neural systems

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
Full-text PDF (327 kB) Citations (26)
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Abstract: A singularly perturbed scalar nonlinear differential-difference equation with two delays is considered that is a mathematical model of an isolated neuron. It is shown that a one-dimensional chain of diffusively coupled oscillators of this type exhibits the well-known buffer phenomenon. Specifically, as the number of chain links increases consistently with decreasing diffusivity, the number of coexisting stable periodic motions in the chain grows indefinitely.
Key words: differential-difference equations, relaxation cycle, autowaves, stability, buffer phenomenon, bursting effect.
Received: 05.12.2011
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 5, Pages 702–719
DOI: https://doi.org/10.1134/S0965542512050090
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in neural systems”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 840–858; Comput. Math. Math. Phys., 52:5 (2012), 702–719
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:54
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