A modification of the Hodgkin--Huxley model and a mathematical interpretation of the principal neurophysiological ``all-or-none'' law
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 66-69
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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.
@article{VMUMM_2021_3_a9,
author = {V. V. Aleksandrov and O. V. Aleksandrova and I. A. Kozik and Yu. S. Semenov},
title = {A modification of the {Hodgkin--Huxley} model and a mathematical interpretation of the principal neurophysiological ``all-or-none'' law},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {66--69},
publisher = {mathdoc},
number = {3},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a9/}
}
TY - JOUR AU - V. V. Aleksandrov AU - O. V. Aleksandrova AU - I. A. Kozik AU - Yu. S. Semenov TI - A modification of the Hodgkin--Huxley model and a mathematical interpretation of the principal neurophysiological ``all-or-none'' law JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2021 SP - 66 EP - 69 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a9/ LA - ru ID - VMUMM_2021_3_a9 ER -
%0 Journal Article %A V. V. Aleksandrov %A O. V. Aleksandrova %A I. A. Kozik %A Yu. S. Semenov %T A modification of the Hodgkin--Huxley model and a mathematical interpretation of the principal neurophysiological ``all-or-none'' law %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2021 %P 66-69 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a9/ %G ru %F VMUMM_2021_3_a9
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 Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 66-69. http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a9/