Mechanics

Study of the modified Hodgkin–Huxley model under the action of stimulation and random noise

V. V. Aleksandrov^a, I. A. Kozik^a, Yu. S. Semenov<sup>b

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Gubkin Russian State University of Oil and Gas

Abstract: In the paper we continue the research on the modified Hodgkin–Huxley model in the presence of random noise. It is shown that, adding a certain short-time stimulation current, a random noise of low amplitude does not prevent the system transition from the motion within a neighborhood of the small stable limit cycle (the mode “None” in accordance with the principal neurophysiological “All or none”–law) to the motion along the big stable limit cycle called “duck nose” (the mode “All” respectively). At the same time, the high amplitude random noise can yield a series of transitions from one regime to the other and vice versa, even for a short-time stimulation. In the absence of stimulation and in the presence of high amplitude noise, such series of transitions were observed earlier during computer simulation.

Key words: Hodgkin–Huxley model, stimulation, random noise.

UDC: 517.93

Received: 27.10.2023

DOI: 10.55959/MSU0579-9368-1-65-2-6

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2024, 79:2, 38–42

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