This article is cited in 2 papers

MATHEMATICS

Properties of an oriented ring of neurons with the Fitzhugh–Nagumo model

E. G. Fedorov

ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia

Abstract: The transmission of an impulse through a neuron is provided by processes that occur at the nanoscale level. This paper will build a model for an oriented ring of connected neurons. To describe the process of impulse transmission through a neuron, the FitzHugh–Nagumo model is used, which allows one to set a higher abstraction level by simulating an impulse. In this case, when transmitting impulses between neurons, the delay is taken into account. For the constructed model, the dependence of the number of neurons on the dynamics of the network as a whole is studied, and local bifurcations are found. All results are verified numerically. It is shown that the period of self-oscillations of such a network depends on the number of neurons.

Keywords: Neural networks, Hopf bifurcations, FitzHugh–Nagumo system, communication delay, stability.

Received: 15.07.2021
Revised: 19.09.2021

Language: English

DOI: 10.17586/2220-8054-2021-12-5-553-562

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