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Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Author

Listed:
  • Yihong Liu

    (School of Computer Science, Huainan Normal University, Huainan 232038, China)

  • Yeguo Sun

    (School of Finance and Mathematics, Huainan Normal University, Huainan 232038, China)

Abstract

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Suggested Citation

  • Yihong Liu & Yeguo Sun, 2024. "Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays," Mathematics, MDPI, vol. 12(7), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1108-:d:1371478
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    References listed on IDEAS

    as
    1. Zhang, Yanlin & Deng, Shengfu, 2019. "Finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 176-190.
    2. Lu, Jiyong & Guo, Yanping & Ji, Yude & Fan, Shuangshuang, 2020. "Finite-time synchronization for different dimensional fractional-order complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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