Geodesic
Local Dynamics of Three Coupled Oscillators with a Feedback Loop
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 105-112.

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

The dynamics of interaction of three neurons is studied. One of possible options of the link is a feedback loop arising at modeling neuronets is considered.
Keywords: feedback loop, normal form method
Mots-clés : bifurcations. 
@article{MAIS_2012_19_3_a6,
     author = {A. O. Tolbey},
     title = {Local {Dynamics} of {Three} {Coupled} {Oscillators} with a {Feedback} {Loop}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a6/}
}
TY  - JOUR
AU  - A. O. Tolbey
TI  - Local Dynamics of Three Coupled Oscillators with a Feedback Loop
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2012
SP  - 105
EP  - 112
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a6/
LA  - ru
ID  - MAIS_2012_19_3_a6
ER  - 
%0 Journal Article
%A A. O. Tolbey
%T Local Dynamics of Three Coupled Oscillators with a Feedback Loop
%J Modelirovanie i analiz informacionnyh sistem
%D 2012
%P 105-112
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a6/
%G ru
%F MAIS_2012_19_3_a6
A. O. Tolbey. Local Dynamics of Three Coupled Oscillators with a Feedback Loop. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 105-112. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a6/

[1] Uri Alon, “Network motifs: theory and experimental approaches”, Nature Genetics, 8 (2007), 450–461 | DOI

[2] R. Milo, S. Shen-Orr, S. Itzkovitz, “Network motifs: Simple Building Blocks of Complex Networks”, Science, 298 (2002), 824–827 | DOI

[3] Yechiam Yemini, The Topology of Biological Networks, Computer Science Department, Columbia University, 2004

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

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

[6] S. D. Glyzin, E. O. Ovsyannikova, “Dvukhchastotnye kolebaniya obobschennogo uravneniya impulsnogo neirona s dvumya zapazdyvaniyami”, Modelirovanie i analiz informatsionnykh sistem, 18:1 (2011), 86–105

[7] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Diskretnye avtovolny v neironnykh sistemakh”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 52:5 (2012), 840–858

[8] S. D. Glyzin, E. O. Kiseleva, “Uchet zapazdyvaniya v tsepochke svyazi mezhdu ostsillyatorami”, Modelirovanie i analiz informatsionnykh sistem, 17:2 (2010), 140–150

[9] S. D. Glyzin, “Relaksatsionnye kolebaniya elektricheski svyazannykh neiropodobnykh ostsillyatorov s zapazdyvaniem”, Modelirovanie i analiz informatsionnykh sistem, 17:2 (2010), 28–47

[10] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “O yavleniyakh khaosa v koltse iz trekh odnonapravlenno svyazannykh generatorov”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 46:10 (2006), 1809–1821 | MR

[11] S. D. Glyzin, A. Yu. Kolesov, Lokalnye metody analiza dinamicheskikh sistem, uchebnoe posobie, Yarosl. gos. un-t, Yaroslavl, 2006, 92 pp.