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Mittag-Leffler synchronization in finite time of fractional-order discrete-time quaternion-valued neural networks via quantized control and its application

Author

Listed:
  • Cheng, Weiwei
  • Zhang, Weiwei
  • Zhang, Hai
  • Stamova, Ivanka
  • Cao, Jinde

Abstract

This paper investigates the finite-time Mittag-Leffler synchronization (FTMLS) of a class of fractional-order discrete-time quaternion-valued neural networks (FODTQNNs) via quantized control. Initially, a FODTQNNs incorporating time delay is established. Due to the strong robustness and adaptability of quantized controllers, we design two types of quantized controllers. Moreover, we combine the quantized controller with an adaptive controller, which significantly reduces control costs. The conditions for finite-time synchronization are derived through the application of inequality techniques and the Razumikhin theorem, by selecting appropriate Lyapunov functions. Eventually, numerical simulations are employed to demonstrate the feasibility of the theoretical analysis presented, and a potential application in image secure communication is presented, demonstrating the practical value of the proposed approach.

Suggested Citation

  • Cheng, Weiwei & Zhang, Weiwei & Zhang, Hai & Stamova, Ivanka & Cao, Jinde, 2026. "Mittag-Leffler synchronization in finite time of fractional-order discrete-time quaternion-valued neural networks via quantized control and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 362-383.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:362-383
    DOI: 10.1016/j.matcom.2026.04.016
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    References listed on IDEAS

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    1. Cui, Xueke & Li, Hong-Li & Zhang, Long & Hu, Cheng & Bao, Haibo, 2023. "Complete synchronization for discrete-time fractional-order coupled neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    3. Shang, Weiying & Zhang, Weiwei & Chen, Dingyuan & Cao, Jinde, 2023. "New criteria of finite time synchronization of fractional-order quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    4. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
    5. Zhang, Hai & Gao, Panqing & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2025. "Fixed/Predefined time synchronization of fractional quaternion delayed neural networks with disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 276-294.
    6. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
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