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Model. Anal. Inform. Sist., 2014, Volume 21, Number 2, Pages 71–89 (Mi mais372)  

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.

Full text: PDF file (977 kB)
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UDC: 517.926
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

Citation in format AMSBIB
\Bibitem{GlyKolRoz14}
\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Non-Classical Relaxation Oscillations in Neurodynamics
\jour Model. Anal. Inform. Sist.
\yr 2014
\vol 21
\issue 2
\pages 71--89
\mathnet{http://mi.mathnet.ru/mais372}


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    This publication is cited in the following articles:
    1. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Self-excited relaxation oscillations in networks of impulse neurons”, Russian Math. Surveys, 70:3 (2015), 383–452  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Моделирование и анализ информационных систем
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