Geodesic
Study of the modified Hodgkin–Huxley model under the action of stimulation and random noise
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 44-47
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMUMM_2024_2_a5,
     author = {V. V. Aleksandrov and I. A. Kozik and Yu. S. Semenov},
     title = {Study of the modified {Hodgkin{\textendash}Huxley} model under the action of stimulation and random noise},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--47},
     year = {2024},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a5/}
}
TY  - JOUR
AU  - V. V. Aleksandrov
AU  - I. A. Kozik
AU  - Yu. S. Semenov
TI  - Study of the modified Hodgkin–Huxley model under the action of stimulation and random noise
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2024
SP  - 44
EP  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a5/
LA  - ru
ID  - VMUMM_2024_2_a5
ER  - 
%0 Journal Article
%A V. V. Aleksandrov
%A I. A. Kozik
%A Yu. S. Semenov
%T Study of the modified Hodgkin–Huxley model under the action of stimulation and random noise
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2024
%P 44-47
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a5/
%G ru
%F VMUMM_2024_2_a5
V. V. Aleksandrov; I. A. Kozik; Yu. S. Semenov. Study of the modified Hodgkin–Huxley model under the action of stimulation and random noise. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 44-47. http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a5/

[1] Aleksandrov V.V., Aleksandrova O.V., Kozik I.A., Semenov Yu.S., “Modifikatsiya modeli Khodzhkina–Khaksli i matematicheskaya interpretatsiya osnovnogo zakona neirofiziologii “Vse ili nichego””, Vestn. Mosk. un-ta. Matem. Mekhan, 2021, no. 3, 66–69 | Zbl

[2] Sadovnichii V.A., Aleksandrov V.V., Aleksandrova T.B. i dr., “Informatsionnyi protsess v lateralnykh polukruzhnykh kanalakh”, Dokl. RAN, 436:1 (2011), 129–132 | MR | Zbl

[3] Tikhonova K.V., Matematicheskie zadachi korrektsii aktivnosti vestibulyarnykh mekhanoretseptorov, Kand. dis., M., 2019 | Zbl

[4] Simiu E., Khaoticheskie perekhody v determinirovannykh i stokhasticheskikh sistemakh. Primenenie metoda Melnikova v tekhnike, fizike i neirofiziologii, Fizmatlit, M., 2007