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Matematicheskie Zametki, 2013, Volume 93, Issue 5, Pages 684–701
DOI: https://doi.org/10.4213/mzm9293 (Mi mzm9293) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Modeling the Bursting Effect in Neuron Systems

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

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
Full-text PDF (581 kB) Citations (26)
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DOI: https://doi.org/10.4213/mzm9293
Abstract: We propose a new method for modeling the well-known phenomenon of “bursting behavior” in neuron systems by invoking delay equations. Namely, we consider a singularly perturbed nonlinear difference-differential equation with two delays describing the functioning of an isolated neuron. Under a suitable choice of parameters, we establish the existence of a stable periodic motion with any prescribed number of spikes on a closed time interval equal to the period length.
Keywords: “bursting behavior” in neuron systems, difference-differential equation, relay equation, Cauchy problem, Schauder principle, relaxation cycle, spiking, stability.
Received: 01.12.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 5, Pages 676–690
DOI: https://doi.org/10.1134/S0001434613050040
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Modeling the Bursting Effect in Neuron Systems”, Mat. Zametki, 93:5 (2013), 684–701; Math. Notes, 93:5 (2013), 676–690
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
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