Nonclassical relaxation oscillations in neurodynamics
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- 作者：S. D. Glyzin ; A. Yu. Kolesov ; N. Kh. Rozov
- 关键词：FitzHugh–Nagumo neuron model ; relaxation cycle ; asymptotics ; stability ; buffering
- 刊名：Automatic Control and Computer Sciences
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：50
- 期：7
- 页码：571-585
- 全文大小：
- 刊物类别：Computer Science
- 刊物主题：Control Structures and Microprogramming;
- 出版者：Allerton Press
- ISSN：1558-108X
- 卷排序：50
文摘
A modification of the well-known FitzHugh–Nagumo model from neuroscience has been proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow variable. The existence and stability of a nonclassical relaxation cycle in this system have been studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A one-dimensional circle of unidirectionally coupled neurons has been considered. The existence of an arbitrarily large number of traveling waves for this chain has been shown. In order to illustrate the increase in the number of stable traveling waves, numerical methods were involved.