On the stability of sets for reaction–diffusion Cohen–Grossberg delayed neural networks

Ivanka Stamova; Gani Stamov

doi:10.3934/dcdss.2020370

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2021, Volume 14, Issue 4: 1429-1446. Doi: 10.3934/dcdss.2020370

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On the stability of sets for reaction–diffusion Cohen–Grossberg delayed neural networks

Ivanka Stamova^, and
Gani Stamov

Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA

^* Corresponding author: Ivanka Stamova
^* Corresponding author: Ivanka Stamova

Received: August 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: April 2021

This paper is supported in part by the European Regional Development Fund through the Operational Programme "Science and Education for Smart Growth" under Contract UNITe No. BG05M2OP001–1.001–0004 (2018–2023)

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Abstract

In this paper, we introduce the notion of stability of sets for reaction-diffusion Cohen–Grossberg neural networks with time-varying delays. The Lyapunov–Razumikhin technique and a comparison principle are adapted to prove the new stability criteria. In addition, the obtained results are extended to the uncertain case, and the robust stability notion is also investigated. Examples are considered to demonstrate the effectiveness of our results.

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Mathematics Subject Classification: Primary: 92B20, 34K20; Secondary: 34K60.

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