Eventually periodic solutions of single neuron model
Articles
Inese Bula
University of Latvia
https://orcid.org/0000-0002-2268-0356
Michael A. Radin
Rochester Institute of Technology
https://orcid.org/0000-0001-9951-7955
Published 2020-11-01
https://doi.org/10.15388/namc.2020.25.20555
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Keywords

neuron model
difference equation
periodic solution
eventually periodic solution

How to Cite

Bula I. and Radin M. A. (2020) “Eventually periodic solutions of single neuron model”, Nonlinear Analysis: Modelling and Control, 25(6), pp. 903-918. doi: 10.15388/namc.2020.25.20555.

Abstract

In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.

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