Lyapunov approach to manifolds stability for impulsive Cohen–Grossberg-type conformable neural network models

Trayan Stamov; Gani Stamov; Ivanka Stamova; Ekaterina Gospodinova; Trayan Stamov; Gani Stamov; Ivanka Stamova; Ekaterina Gospodinova

doi:10.3934/mbe.2023689

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 15431-15455. doi: 10.3934/mbe.2023689

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Lyapunov approach to manifolds stability for impulsive Cohen–Grossberg-type conformable neural network models

1.
Department of Engineering Design, Technical University of Sofia, Sofia 1000, Bulgaria
2.
Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio TX 78249, USA
3.
Department of Computer Sciences, Technical University of Sofia, Sliven 8800, Bulgaria

Received: 16 May 2023 Revised: 05 July 2023 Accepted: 18 July 2023 Published: 24 July 2023

In this paper, motivated by the advantages of the generalized conformable derivatives, an impulsive conformable Cohen–Grossberg-type neural network model is introduced. The impulses, which can be also considered as a control strategy, are at fixed instants of time. We define the notion of practical stability with respect to manifolds. A Lyapunov-based analysis is conducted, and new criteria are proposed. The case of bidirectional associative memory (BAM) network model is also investigated. Examples are given to demonstrate the effectiveness of the established results.
- Cohen–Grossberg neural networks,
- conformable derivative,
- impulses,
- manifolds,
- practical stability
Citation: Trayan Stamov, Gani Stamov, Ivanka Stamova, Ekaterina Gospodinova. Lyapunov approach to manifolds stability for impulsive Cohen–Grossberg-type conformable neural network models[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 15431-15455. doi: 10.3934/mbe.2023689

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Abstract

In this paper, motivated by the advantages of the generalized conformable derivatives, an impulsive conformable Cohen–Grossberg-type neural network model is introduced. The impulses, which can be also considered as a control strategy, are at fixed instants of time. We define the notion of practical stability with respect to manifolds. A Lyapunov-based analysis is conducted, and new criteria are proposed. The case of bidirectional associative memory (BAM) network model is also investigated. Examples are given to demonstrate the effectiveness of the established results.

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