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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 5, Pages 840–858
(Mi zvmmf9713)
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This article is cited in 26 scientific papers (total in 26 papers)
Discrete autowaves in neural systems
S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb a Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia
Abstract:
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.
Key words:
differential-difference equations, relaxation cycle, autowaves, stability, buffer phenomenon, bursting effect.
Received: 05.12.2011
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in neural systems”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 840–858; Comput. Math. Math. Phys., 52:5 (2012), 702–719
Linking options:
https://www.mathnet.ru/eng/zvmmf9713 https://www.mathnet.ru/eng/zvmmf/v52/i5/p840
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Abstract page: | 380 | Full-text PDF : | 104 | References: | 52 | First page: | 14 |
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