Geodesic
Relaxation oscillations of electrically coupled neuron-like systems with delay
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 2, pp. 28-47.

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

The system of diffusion coupled nonlinear differential-difference equations with delay modelling the electrical interaction of pulse neurons is studied. Given the speed of electrical processes in the system is high, the limit system, responsible for relaxation cycles, is constructed. Along with a synchronous cycle the system permits stable asynchronous cycles, which asymptotics are presented.
Mots-clés : relaxation oscillations, bifurcations.
Keywords: spiking neuron, differential-difference equation 
@article{MAIS_2010_17_2_a2,
     author = {S. D. Glyzin},
     title = {Relaxation oscillations of electrically coupled neuron-like systems with delay},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {28--47},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2010_17_2_a2/}
}
TY  - JOUR
AU  - S. D. Glyzin
TI  - Relaxation oscillations of electrically coupled neuron-like systems with delay
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2010
SP  - 28
EP  - 47
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2010_17_2_a2/
LA  - ru
ID  - MAIS_2010_17_2_a2
ER  - 
%0 Journal Article
%A S. D. Glyzin
%T Relaxation oscillations of electrically coupled neuron-like systems with delay
%J Modelirovanie i analiz informacionnyh sistem
%D 2010
%P 28-47
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2010_17_2_a2/
%G ru
%F MAIS_2010_17_2_a2
S. D. Glyzin. Relaxation oscillations of electrically coupled neuron-like systems with delay. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 2, pp. 28-47. http://geodesic.mathdoc.fr/item/MAIS_2010_17_2_a2/

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

[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] E. F. Mischenko, L. S. Pontryagin, “Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkie k razryvnym”, DAN SSSR, 102:5 (1955), 889–891

[4] E. F. Mischenko, “Asimptoticheskoe vychislenie periodicheskikh reshenii sistem differentsialnykh uravnenii, soderzhaschikh malye parametry pri proizvodnykh”, Izv. AN SSSR. Ser. matem., 21:5 (1957), 627–654

[5] E. F. Mischenko, L. S. Pontryagin, “Dokazatelstvo nekotorykh asimptoticheskikh formul dlya reshenii differentsialnykh uravnenii s malym parametrom”, DAN SSSR, 120:5 (1958), 967–969

[6] E. F. Mischenko, L. S. Pontryagin, “Vyvod nekotorykh asimptoticheskikh otsenok dlya reshenii differentsialnykh uravnenii s malym parametrom pri proizvodnykh”, Izv. AN SSSR. Ser. matem., 23:5 (1959), 643–660

[7] L. S. Pontryagin, “Asimptoticheskoe povedenie reshenii sistem differentsialnykh uravnenii s malym parametrom pri vysshikh proizvodnykh”, Izv. AN SSSR. Ser. matem., 21:5 (1957), 605–626 | MR | Zbl

[8] E. F. Mischenko, N. Kh. Rozov, Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Nauka, M., 1975, 248 pp. | MR

[9] E. F. Mischenko, Yu. C. Kolesov, A. Yu. Kolesov, N. Kh. Rozov, Periodicheskie dvizheniya i bifurkatsionnye protsessy v singulyarno vozmuschennykh sistemakh, Fizmatlit, M., 1995, 336 pp. | MR

[10] Yu. C. Kolesov, A. Yu. Kolesov, Relaksatsionnye kolebaniya v matematicheskikh modelyakh ekologii, Tr. MIAN, 199, Nauka, M., 1993, 125 pp. | Zbl

[11] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, “Rele s zapazdyvaniem i ego $C^1$-approksimatsiya”, Tr. MIAN, 216, 1997, 126–153 | MR | Zbl