Open AccessEventually periodic solutions of single neuron model
Author(s) -
Inese Bula,
Michael A. Radin
Publication year - 2020
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2020.25.20555
Subject(s) - periodic function , period (music) , mathematics , piecewise , biological neuron model , piecewise linear function , mathematical analysis , computer science , physics , artificial neural network , artificial intelligence , acoustics
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.