Dynamic behavior for a group of biological neurons FitzHugh-Nagumo

Title	Dynamic behavior for a group of biological neurons FitzHugh-Nagumo
Authors	E. G. Fedorov¹, I. Y. Popov¹ ¹ITMO University
Annotation	In this paper, a connected and oriented ring of neurons will be considered. For such a configuration, the dependence of the dynamics of the system on the delay in impulse transmission between neurons and on the number of neurons in the ring is studied. To describe a neuron, the FitzHugh-Nagumo model is used, as a model capable of describing the main features of a biological neuron and, at the same time, is computationally relatively simple. The results obtained are verified numerically. As a result, it was shown that there is no rectilinear dependence of the period of passage of the pulse along the ring on the number of neurons in the ring. Criteria for determining local bifurcations are also obtained.
Keywords	FitzHugh-Nagumo system, time delay, neural networks, stability, Hopf bifurcations.
Citation	Fedorov E. G., Popov I. Y. ''Dynamic behavior for a group of biological neurons FitzHugh-Nagumo'' [Electronic resource]. Proceedings of the XV International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 15-18, 2021). Saransk: SVMO Publ, 2021. - pp. 190-203. Available at: https://conf.svmo.ru/files/2021/papers/article07.pdf. - Date of access: 03.12.2024.