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Russian Mathematical Surveys, 2015, Volume 70, Issue 3, Pages 383–452
DOI: https://doi.org/10.1070/RM2015v070n03ABEH004951 (Mi rm9659) 		 
This article is cited in 43 scientific papers (total in 43 papers)

Self-excited relaxation oscillations in networks of impulse neurons

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

a Yaroslavl State University
b Moscow State University
English version PDF (1138 kB) Citations (43)
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DOI: https://doi.org/10.1070/RM2015v070n03ABEH004951
Abstract: This paper addresses the problem of mathematical modelling of neuron activity. New classes of singularly perturbed differential-difference equations with Volterra-type delay are proposed and used to describe how single neurons and also neural networks function with various kinds of connections (electrical or chemical). Special asymptotic methods are developed which make it possible to analyse questions of the existence and stability of relaxation periodic motions in such systems.
Bibliography: 56 titles.
Keywords: neuron models, differential-difference equations, asymptotic behaviour, relaxation oscillations, stability, buffering, bursting effect.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-04066-а
Ministry of Education and Science of the Russian Federation 1875 № 2014/258
Received: 05.02.2015
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 3(423), Pages 3–76
DOI: https://doi.org/10.4213/rm9659
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34C26, 34K26, 92C20
Language: English
Original paper language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Self-excited relaxation oscillations in networks of impulse neurons”, Uspekhi Mat. Nauk, 70:3(423) (2015), 3–76; Russian Math. Surveys, 70:3 (2015), 383–452
Citation in format AMSBIB
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    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1035
    Russian version PDF:412
    English version PDF:41
    References:82
    First page:53
     
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