Geodesic
Mathematical model of propagation of nerve impulses with regard hereditarity
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2017), pp. 33-43 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A mathematical model of the propagation of the nervous pulse of FitzHugh-Nagumo is proposed, which takes into account the effect of heredity. This hereditary model is described by an integro-differential equation with a power kernel - a function of memory. The algorithm for the numerical solution of this model is implemented in a computer program in the environment of symbolic mathematics Maple. With the help of this program, calculated curves - oscillograms, and also phase trajectories were constructed depending on various values of control parameters.
Keywords: hereditarity Model FitzHugh-Nagumo, finite-difference scheme. 
@article{VKAM_2017_1_a3,
     author = {O. D. Lipko},
     title = {Mathematical model of propagation of nerve impulses with regard hereditarity},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {33--43},
     year = {2017},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2017_1_a3/}
}
TY  - JOUR
AU  - O. D. Lipko
TI  - Mathematical model of propagation of nerve impulses with regard hereditarity
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2017
SP  - 33
EP  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VKAM_2017_1_a3/
LA  - ru
ID  - VKAM_2017_1_a3
ER  - 
%0 Journal Article
%A O. D. Lipko
%T Mathematical model of propagation of nerve impulses with regard hereditarity
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2017
%P 33-43
%N 1
%U http://geodesic.mathdoc.fr/item/VKAM_2017_1_a3/
%G ru
%F VKAM_2017_1_a3
O. D. Lipko. Mathematical model of propagation of nerve impulses with regard hereditarity. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2017), pp. 33-43. http://geodesic.mathdoc.fr/item/VKAM_2017_1_a3/

[1] Volterra V., “Sur les 'equations int'egro-diff'erentielles et leurs applications”, Acta Mathematica, 35:1 (1912), 295–356 | DOI | MR | Zbl

[2] Uchajkin V. V., Metod drobnyh proizvodnyh, Artishok, Ul'janovsk, 2008, 512 pp.

[3] Parovik R. I., Matematicheskoe modelirovanie linejnyh jereditarnyh oscilljatorov, KamGU im. Vitusa Beringa, Petropavlovsk-Kamchatskij, 2015, 178 pp.

[4] Petras I., Fractional-Order Nonlinear Systems. Modeling, Analysis and Simulation, Beijing and Springer-Verlag, Berlin–Heidelberg, 2011, 218 pp. | Zbl

[5] FitzHugh R., “Impulses and physiological states in theoretical models of nerve membrane”, Biophysical Journal, 1 (1961), 446–446 | DOI

[6] Nagumo J., Arimoto S., Yoshizawa S., “An active pulse transmission line simulating nerve axon”, Proc. IRE, 50 (1962), 2061–2070 | DOI

[7] Lipko O. D., “Ereditarnoe modelnoe uravnenie FittsKhyu-Nagumo”, Mezhdunarodnyi studencheskii nauchnyi vestnik, 2017, no. 2, 43-43

[8] Parovik R.I., “Mathematical modeling of nonlocal oscillatory Duffing system with fractal friction”, Bulletin KRASEC. Physical and Mathematical Sciences, 10:1 (2015), 16-21

[9] Parovik R. I., “Ob issledovanii ustojchivosti jereditarnogo oscilljatora Van der Polja”, Fundamental'nye issledovanija, 2016, no. 3(2), 283–287

[10] Parovik R. I., “Explicit finite-difference scheme for the numerical solution of the model equation of nonlinear hereditary oscillator with variable order fractional derivatives”, Archives of Control Sciences, 26:3 (2016), 429–435 | DOI

[11] Parovik R.I., “Finite-difference schemes for fractal oscillator with a variable fractional order”, Bulletin KRASEC. Physical and Mathematical Sciences, 11:2 (2015), 85-92