Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

M. Syed Ali, Gani Stamov (), Ivanka Stamova, Tarek F. Ibrahim, Arafa A. Dawood and Fathea M. Osman Birkea
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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
Tarek F. Ibrahim: Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha 62529, Saudi Arabia
Arafa A. Dawood: Department of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha 62529, Saudi Arabia
Fathea M. Osman Birkea: Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia

Mathematics, 2023, vol. 11, issue 20, 1-24

Abstract: In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results.

Keywords: fractional-order system; bidirectional associative memory neural networks; distributed delays; global asymptotic stability; global Mittag–Leffler stability; reaction–diffusion terms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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