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Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays

Author

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  • Grienggrai Rajchakit

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand)

  • Ramalingam Sriraman

    (Department of Mathematics, Thiruvalluvar University, Vellore 632115, India)

  • Chee Peng Lim

    (Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia)

  • Panu Sam-ang

    (School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand)

  • Porpattama Hammachukiattikul

    (Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand)

Abstract

In this paper, we explore the finite-time synchronization of Clifford-valued neural networks with finite-time distributed delays. To address the problem associated with non-commutativity pertaining to the multiplication of Clifford numbers, the original n -dimensional Clifford-valued drive and response systems are firstly decomposed into the corresponding 2 m -dimensional real-valued counterparts. On the basis of a new Lyapunov–Krasovskii functional, suitable controller and new computational techniques, finite-time synchronization criteria are formulated for the corresponding real-valued drive and response systems. The feasibility of the main results is verified by a numerical example.

Suggested Citation

  • Grienggrai Rajchakit & Ramalingam Sriraman & Chee Peng Lim & Panu Sam-ang & Porpattama Hammachukiattikul, 2021. "Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1163-:d:559450
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    References listed on IDEAS

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    1. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    2. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    3. Yongkun Li & Jianglian Xiang, 2019. "Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    4. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
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    Cited by:

    1. Pengfei Guo & Yunong Zhang, 2022. "Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-," Mathematics, MDPI, vol. 10(9), pages 1-27, April.
    2. Weiwei Qi & Yongkun Li, 2022. "Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    3. Shen, Shiping & Meng, Xiaofang, 2023. "Finite-time stability of almost periodic solutions of Clifford-valued RNNs with time-varying delays and D operator on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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