Discrete autowaves in neural systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 840-858 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A singularly perturbed scalar nonlinear differential-difference equation with two delays is considered that is a mathematical model of an isolated neuron. It is shown that a one-dimensional chain of diffusively coupled oscillators of this type exhibits the well-known buffer phenomenon. Specifically, as the number of chain links increases consistently with decreasing diffusivity, the number of coexisting stable periodic motions in the chain grows indefinitely.
@article{ZVMMF_2012_52_5_a7,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Discrete autowaves in neural systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {840--858},
     year = {2012},
     volume = {52},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a7/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - Discrete autowaves in neural systems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 840
EP  - 858
VL  - 52
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a7/
LA  - ru
ID  - ZVMMF_2012_52_5_a7
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T Discrete autowaves in neural systems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 840-858
%V 52
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a7/
%G ru
%F ZVMMF_2012_52_5_a7
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Discrete autowaves in neural systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 840-858. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a7/

[1] Chay T. R., Rinzel J., “Bursting, beating, and chaos in an excitable membrane model”, Biophys. J., 47:3 (1985), 357–366 | DOI

[2] Ermentrout G. B., Kopell N., “Parabolic bursting in an excitable system coupled with a slow oscillation”, SIAM J. Appl. Math., 46:2 (1986), 233–253 | DOI | MR | Zbl

[3] Izhikevich E., “Neural excitability, spiking and bursting”, Internat. J. Bifurcation and Chaos, 10:6 (2000), 1171–1266 | DOI | MR | Zbl

[4] Rabinovich M. I., Varona P., Selverston A. I., Abarbanel H. D. I., “Dynamical principles in neuroscience”, Rev. Mod. Phys., 78:4 (2006), 1213–1265 | DOI | MR

[5] Coombes S., Bressloff P. C., Bursting: the genesis of rhythm in the nervous system, World Scientific Publishing Company, 2005 | MR

[6] Kolesov A. Yu., Rozov N. Kh., Invariantnye tory nelineinykh volnovykh uravnenii, Fizmatlit, M., 2004

[7] Mischenko E. F., Sadovnichii V. A., Kolesov A. Yu., Rozov N. Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei, Fizmatlit, M., 2005

[8] Kaschenko S. A., Maiorov V. V., Modeli volnovoi pamyati, Knizhnyi dom “LIBROKOM”, M., 2009

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

[10] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Ob odnoi modifikatsii uravneniya Khatchinsona”, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2009–2112 | MR

[11] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Relaksatsionnye avtokolebaniya v neironnykh sistemakh, I”, Differents. ur-niya, 47:7 (2011), 919–932 | MR | Zbl

[12] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Relaksatsionnye avtokolebaniya v neironnykh sistemakh, II”, Differents. ur-niya, 47:12 (2011), 1675–1692 | MR | Zbl