Non-Classical Relaxation Oscillations in Neurodynamics

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 slo...

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Bibliographic Details
Main Authors: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov
Format: Article
Language:English
Published: Yaroslavl State University 2014-04-01
Series:Моделирование и анализ информационных систем
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Online Access:https://www.mais-journal.ru/jour/article/view/121
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Summary: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 δ-like function. A onedimensional 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.
ISSN:1818-1015
2313-5417