Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 3, Pages 66–69 (Mi vmumm4406)  
This article is cited in 1 scientific paper (total in 1 paper)

Mechanics

A modification of the Hodgkin–Huxley model and a mathematical interpretation of the principal neurophysiological “all-or-none” law

V. V. Aleksandrova, O. V. Aleksandrovaa, I. A. Kozika, Yu. S. Semenovb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Russian University of Transport
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Abstract: In the paper we present the results of numerical simulation for the simplified and modified Hodgkin–Huxley model of primary afferent neuron in the presence of stochastic noise. The transitions from the attraction domain of the stationary point — the stable focus — to the attraction domain of the periodic attractor and back to the attraction domain of the focus are considered. Such transitions can alternate many times, which is the mathematical interpretation of the principal neurophysiological all-or-none law.
Key words: Hodgkin–Huxley model, phase trajectory, limit cycle, random noise.
Received: 11.11.2020
English version:
Moscow University Mechanics Bulletin, 2021, Volume 76, Issue 3, Pages 78–82
DOI: https://doi.org/10.3103/S002713302103002X
Bibliographic databases:
Document Type: Article
UDC: 517.93
Language: Russian
Citation: V. V. Aleksandrov, O. V. Aleksandrova, I. A. Kozik, Yu. S. Semenov, “A modification of the Hodgkin–Huxley model and a mathematical interpretation of the principal neurophysiological “all-or-none” law”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 3, 66–69; Moscow University Mechanics Bulletin, 76:3 (2021), 78–82
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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