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Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

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  • Chen, Yonghui
  • Zhang, Xian
  • Xue, Yu

Abstract

In this paper, the synchronization control problem of high-order quaternion Hopfield neural networks (HOQHNNs) with unbounded distributed delays and time-varying discrete delays is studied. Since the non-exchangeability of quaternion multiplication operation, the error system is first decomposed into equivalent real-valued systems, and then the driving-response structure of HOQHNN is achieved exponential synchronization by designing a state feedback controller. At the same time, two examples are offered to illustrate the applicability of the consequences obtained. Finally, the obtained global exponential synchronization criterion is applied to encrypt and decrypt color images. The method proposed here has four advantages: (1) There is no need to construct any Lyapunov–Krasovskii functional, which is straight in the light of the definition of global exponential synchronization; (2) The obtained synchronization criterion contains only a few simple inequalities, which can find the solutions readily; (3) The proposed method is available to real-valued and complex-valued neural networks; (4) The obtained results are helpful for the image secure transmission.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:173-189
    DOI: 10.1016/j.matcom.2021.10.012
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    References listed on IDEAS

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    5. Hassan Ghiti Sarand & Bahram Karimi, 2016. "Synchronisation of high-order MIMO nonlinear systems using distributed neuro-adaptive control," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(9), pages 2214-2224, July.
    6. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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    Cited by:

    1. Meng, Xianhe & Zhang, Xian & Wang, Yantao, 2023. "Bounded real lemmas and exponential H∞ control for memristor-based neural networks with unbounded time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 66-81.
    2. Yang, Jinrong & Chen, Guici & Wen, Shiping & Wang, Leimin, 2023. "Finite-time dissipative control for discrete-time memristive neural networks via interval matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Chen, Yonghui & Xue, Yu & Yang, Xiaona & Zhang, Xian, 2023. "A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Zhang, Hai & Cheng, Yuhong & Zhang, Weiwei & Zhang, Hongmei, 2023. "Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 846-857.
    5. Zhang, Zhongjie & Yu, Tingting & Zhang, Xian, 2022. "Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    6. Chang, Shuang & Wang, Yantao & Zhang, Xian & Wang, Xin, 2023. "A new method to study global exponential stability of inertial neural networks with multiple time-varying transmission delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 329-340.
    7. Feifei Yang & Xikui Hu & Guodong Ren & Jun Ma, 2023. "Synchronization and patterns in a memristive network in noisy electric field," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-14, June.

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