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Modelirovanie i Analiz Informatsionnykh Sistem, 2014, Volume 21, Number 2, Pages 71–89
(Mi mais372)
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This article is cited in 1 scientific paper (total in 1 paper)
Non-Classical Relaxation Oscillations in Neurodynamics
S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb a P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
b M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia
Abstract:
A modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a $\delta$-like function. A one-dimensional circle of unidirectionally coupled neurons is considered. It is shown the existence of an arbitrarily large number of traveling waves for this chain. In order to illustrate the increasing of the number of stable traveling waves numerical methods were involved.
Keywords:
impuls neuron, FitzHugh–Nagumo model, relaxation cycle, asymptotics, stability, buffering.
Received: 10.11.2013
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Non-Classical Relaxation Oscillations in Neurodynamics”, Model. Anal. Inform. Sist., 21:2 (2014), 71–89
Linking options:
https://www.mathnet.ru/eng/mais372 https://www.mathnet.ru/eng/mais/v21/i2/p71
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Abstract page: | 344 | Full-text PDF : | 120 | References: | 63 |
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