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Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

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  • Jibin Yang

    (Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
    Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Xihua University, Chengdu 610039, China)

  • Xiaohui Xu

    (Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
    Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Xihua University, Chengdu 610039, China)

  • Quan Xu

    (School of Mechanical Engineering, Xihua University, Chengdu 610039, China)

  • Haolin Yang

    (Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China)

  • Mengge Yu

    (College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

Abstract

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Suggested Citation

  • Jibin Yang & Xiaohui Xu & Quan Xu & Haolin Yang & Mengge Yu, 2024. "Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances," Mathematics, MDPI, vol. 12(6), pages 1-26, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:917-:d:1360550
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    References listed on IDEAS

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    1. Yu, Siyi & Li, Hua & Chen, Xiaofeng & Lin, Dongyuan, 2023. "Multistability analysis of quaternion-valued neural networks with cosine activation functions," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    2. 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).
    3. Zhang, Xiao-Li & Li, Hong-Li & Kao, Yonggui & Zhang, Long & Jiang, Haijun, 2022. "Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    4. Kiruthika, R. & Krishnasamy, R. & Lakshmanan, S. & Prakash, M. & Manivannan, A., 2023. "Non-fragile sampled-data control for synchronization of chaotic fractional-order delayed neural networks via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Mo, Wenjun & Bao, Haibo, 2022. "Finite-time synchronization for fractional-order quaternion-valued coupled neural networks with saturated impulse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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