Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control

M. Hymavathi, Tarek F. Ibrahim (), M. Syed Ali (), Gani Stamov, Ivanka Stamova (), B. A. Younis and Khalid I. Osman
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M. Hymavathi: Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India
Tarek F. Ibrahim: Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha, Saudi Arabia
M. Syed Ali: Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India
Gani Stamov: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
B. A. Younis: Department of Mathematics, Faculty of Sciences and Arts in Zahran Alganoob, King Khalid University, Abha, Saudi Arabia
Khalid I. Osman: Department of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha, Saudi Arabia

Mathematics, 2022, vol. 10, issue 20, 1-18

Abstract: This paper introduces a novel synchronization scheme for fractional-order neural networks with time delays and reaction-diffusion terms via pinning control. We consider Caputo fractional derivatives, constant delays and distributed delays in our model. Based on the stability behavior, fractional inequalities and Lyapunov-type functions, several criteria are derived, which ensure the achievement of a synchronization for the drive-response systems. The obtained criteria are easy to test and are in the format of inequalities between the system parameters. Finally, numerical examples are presented to illustrate the results. The obtained criteria in this paper consider the effect of time delays as well as the reaction-diffusion terms, which generalize and improve some existing results.

Keywords: synchronization; neural network models; fractional derivatives; time delays; reaction-diffusion terms; pinning control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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