A nonlinear version of the distributed Halanay inequality and its application

Nasser eddine Tatar; Rathinasamy Sakthivel

doi:10.1002/mma.7917

A nonlinear version of the distributed Halanay inequality and its application

Nasser eddine Tatar, Rathinasamy Sakthivel^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non-Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.

Original language	English
Pages (from-to)	2190-2203
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	45
Issue number	4
DOIs	https://doi.org/10.1002/mma.7917
State	Published - 15 Mar 2022

Bibliographical note

Funding Information:
The first author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals (Interdisciplinary Research Center for Intelligent Manufacturing & Robotics) through the project No. SB201006.

Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.

Keywords

Hopfield neural network
Non-Lipschitz continuous activation functions
exponential stabilization
nonlinear Halanay inequality

ASJC Scopus subject areas

Mathematics (all)
Engineering (all)

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10.1002/mma.7917

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title = "A nonlinear version of the distributed Halanay inequality and its application",

abstract = "In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non-Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.",

keywords = "Hopfield neural network, Non-Lipschitz continuous activation functions, exponential stabilization, nonlinear Halanay inequality",

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AU - Sakthivel, Rathinasamy

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N2 - In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non-Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.

AB - In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non-Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.

KW - Hopfield neural network

KW - Non-Lipschitz continuous activation functions

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ER -

A nonlinear version of the distributed Halanay inequality and its application

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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