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Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay

Author

Listed:
  • Shichao Jia

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Cheng Hu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China)

  • Haijun Jiang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China)

Abstract

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria.

Suggested Citation

  • Shichao Jia & Cheng Hu & Haijun Jiang, 2023. "Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay," Mathematics, MDPI, vol. 11(23), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4825-:d:1290870
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    References listed on IDEAS

    as
    1. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Enli Wu & Yao Wang & Yundong Li & Kelin Li & Fei Luo, 2023. "Fixed-Time Synchronization of Complex-Valued Coupled Networks with Hybrid Perturbations via Quantized Control," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    3. Amir Rezaie & Saleh Mobayen & Mohammad Reza Ghaemi & Afef Fekih & Anton Zhilenkov, 2023. "Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-14, July.
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