Math. Model. Nat. Phenom.
Volume 16, 2021
Nonlocal and delay equations
|Number of page(s)||20|
|Published online||11 May 2021|
Asymptotic behavior of a BAM neural network with delays of distributed type
Laboratory of SDG, Faculty of Mathematics, University of Science and Technology Houari Boumedienne,
P.O. Box 32, El-Alia
2 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia.
* Corresponding author: firstname.lastname@example.org
Accepted: 24 April 2021
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.
Mathematics Subject Classification: 34A40 / 92B20 / 34A34 / 34C11 / 34D05 / 34D20
Key words: Exponential stability / BAM neural network / distributed delay / nonlinear Halanay inequality
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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