Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument

Abstract

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

An investigation on the Lasota-Wazewska model with a piecewise constant argument

“…These type of equations have attracted great deal of attention because they combine the properties of both continuous and discrete dynamical systems. In mathematical modelling considering both continuous and discrete times makes sense so the use of piecewise constant arguments come into question, see [2,4,7,13,21,25,42,50,55,61] and the references therein. To the best of our knowledge the Lasota-Wazewska model with a piecewise constant argument was considered in [9], [12] and [51].…”