Geodesic
Quasi-periodic oscillations of a neuron equation with two delays
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 1, pp. 86-105.

Voir la notice de l'article provenant de la source Math-Net.Ru

The dynamics of a generalized impulse neuron equation with two delays is studied. A local analysis of a loss of stability for a nonzero equilibrium state has been made. Phase reorganizations have been numerically analyzed with the help of the obtained asymptotic formulas.
Mots-clés : delay; normal form; bifurcations; autooscillations. 
@article{MAIS_2011_18_1_a8,
     author = {S. D. Glyzin and E. O. Ovsyannikova},
     title = {Quasi-periodic oscillations of a neuron equation with two delays},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {86--105},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a8/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - E. O. Ovsyannikova
TI  - Quasi-periodic oscillations of a neuron equation with two delays
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2011
SP  - 86
EP  - 105
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a8/
LA  - ru
ID  - MAIS_2011_18_1_a8
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A E. O. Ovsyannikova
%T Quasi-periodic oscillations of a neuron equation with two delays
%J Modelirovanie i analiz informacionnyh sistem
%D 2011
%P 86-105
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a8/
%G ru
%F MAIS_2011_18_1_a8
S. D. Glyzin; E. O. Ovsyannikova. Quasi-periodic oscillations of a neuron equation with two delays. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 1, pp. 86-105. http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a8/

[1] A. L. Hodgkin, A. F. Huxley, “A quantitative description of membrane current and application to conduction and excitation in nerve”, Journal Physiol., 117 (1952), 500–544

[2] S. A. Kaschenko, V. V. Maiorov, “Ob odnom differentsialno-raznostnom uravnenii, modeliruyuschem impulsnuyu aktivnost neirona”, Matematicheskoe modelirovanie, 5:12 (1993), 13–25 | MR

[3] V. V. Maiorov, I. Yu. Myshkin, “Matematicheskoe modelirovanie neironov seti na osnove uravnenii s zapazdyvaniem”, Matematicheskoe modelirovanie, 2:11 (1990), 64–76 | MR

[4] E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, Cambridge, Mass., 2007 | MR

[5] S. D. Glyzin, “Dvukhchastotnye kolebaniya fundamentalnogo uravneniya dinamiki populyatsii nasekomykh”, Nelineinye kolebaniya i ekologiya, Mezhvuz. sb., Yarosl. un-t., Yaroslavl, 1984, 91–116 | MR

[6] S. D. Glyzin, “Uchet vozrastnykh grupp v uravnenii Khatchinsona”, Modelirovanie i analiz informatsionnykh sistem, 14:3 (2007), 29–42

[7] S. D. Glyzin, E. O. Kiseleva, “Dinamika vzaimodeistviya pary ostsillyatorov neironnogo tipa”, Modelirovanie i analiz informatsionnykh sistem, 15:2 (2008), 75–88