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Fixed-time synchronization of quaternion-valued neural networks

Author

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  • Deng, Hui
  • Bao, Haibo

Abstract

In this paper, the fixed-time synchronization problem of quaternion-valued neural networks is investigated. Different from the finite-time synchronization related to the initial conditions, the settling time of fixed-time synchronization can be changed properly according to the actual needs. The fixed-time synchronization of quaternion-valued neural networks is firstly studied by adding the new nonlinear feedback controllers and employing the theorem of fixed-time stability. The quaternion-valued neural network is addressed by dividing the system under investigation into four real-valued parts. Then based on related theorem of fixed-time stability, and selecting the appropriate controllers and Lyapunov function, sufficient conditions of fixed-time synchronization for quaternion-valued neural networks are obtained. In the same way, the results of finite-time synchronization can also be got. Finally, one numerical example is provided to illustrate the effectiveness of the proposed results.

Suggested Citation

  • Deng, Hui & Bao, Haibo, 2019. "Fixed-time synchronization of quaternion-valued neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    • Handle: RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307976
    DOI: 10.1016/j.physa.2019.121351
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    Citations

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    Cited by:

    1. Liu, Xinmiao & Xia, Jianwei & Huang, Xia & Shen, Hao, 2020. "Generalized synchronization for coupled Markovian neural networks subject to randomly occurring parameter uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Zhang, Weiwei & Sha, Chunlin & Cao, Jinde & Wang, Guanglan & Wang, Yuan, 2021. "Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    3. 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).
    4. Jun Guo & Yanchao Shi & Weihua Luo & Yanzhao Cheng & Shengye Wang, 2023. "Adaptive Global Synchronization for a Class of Quaternion-Valued Cohen-Grossberg Neural Networks with Known or Unknown Parameters," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
    5. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    6. Mairemunisa Abudusaimaiti & Abuduwali Abudukeremu & Amina Sabir, 2023. "Fixed/Preassigned-Time Stochastic Synchronization of Complex-Valued Fuzzy Neural Networks with Time Delay," Mathematics, MDPI, vol. 11(17), pages 1-18, September.
    7. Juan Yu & Kailong Xiong & Cheng Hu, 2024. "Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique," Mathematics, MDPI, vol. 12(7), pages 1-22, March.
    8. Chen, Yonghui & Zhang, Xian & Xue, Yu, 2022. "Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 173-189.

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