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

Author

Listed:
  • 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)

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.

Suggested Citation

  • M. Syed Ali & Gani Stamov & Ivanka Stamova & Tarek F. Ibrahim & Arafa A. Dawood & Fathea M. Osman Birkea, 2023. "Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers," Mathematics, MDPI, vol. 11(20), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4248-:d:1257792
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    References listed on IDEAS

    as
    1. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
    2. Bohner, Martin & Jonnalagadda, Jagan Mohan, 2022. "Discrete fractional cobweb models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Hongyun Yan & Yuanhua Qiao & Lijuan Duan & Ling Zhang, 2020. "Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, August.
    4. Li, Ruoxia & Gao, Xingbao & Cao, Jinde, 2019. "Non-fragile state estimation for delayed fractional-order memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 221-233.
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