Asymptotic behavior of a BAM neural network with delays of distributed type

¹ Laboratory of SDG, Faculty of Mathematics, University of Science and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria.
² Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia.

^* Corresponding author: sothmani@usthb.dz

Received: 11 April 2020
Accepted: 24 April 2021

Abstract

In this paper, we examine a Bidirectional Associative Memory neural network model with distributed delays. Using a result due to Cid [J. Math. Anal. Appl. 281 (2003) 264–275], we were able to prove an exponential stability result in the case when the standard Lipschitz continuity condition is violated. Indeed, we deal with activation functions which may not be Lipschitz continuous. Therefore, the standard Halanay inequality is not applicable. We will use a nonlinear version of this inequality. At the end, the obtained differential inequality which should imply the exponential stability appears ‘state dependent’. That is the usual constant depends in this case on the state itself. This adds some difficulties which we overcome by a suitable argument.