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Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control

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  • Sun, Yuting
  • Hu, Cheng
  • Yu, Juan
  • Shi, Tingting

Abstract

This article studies the synchronization issue of fractional reaction-diffusion neural networks (FRDNNs) with time delay and mixed boundary condition. First, a novel boundary controller with constant-valued gain is designed, which only relies on the boundary state information. Subsequently, by virtue of Lyapunov direct technique and LMI approach, the Mittag–Leffler synchronization conditions are established. Besides, to effectively regulate the control gain, a fractional-order adaptive boundary controller is developed and the adaptive synchronization of FRDNNs is rigorously analyzed. Note that, the above control strategies are also workable for traditional integer-order reaction-diffusion neural networks. The developed theoretical analysis is supported eventually via a numerical example.

Suggested Citation

  • Sun, Yuting & Hu, Cheng & Yu, Juan & Shi, Tingting, 2023. "Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001510
    DOI: 10.1016/j.amc.2023.127982
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    References listed on IDEAS

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    1. Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
    2. Hu, Cheng & Yu, Juan, 2016. "Generalized intermittent control and its adaptive strategy on stabilization and synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 262-269.
    3. Chen, Wei & Yu, Yongguang & Hai, Xudong & Ren, Guojian, 2022. "Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Chang, Wenting & Zhu, Song & Li, Jinyu & Sun, Kaili, 2018. "Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 346-362.
    5. Giona, Massimiliano & Cerbelli, Stefano & Roman, H.Eduardo, 1992. "Fractional diffusion equation and relaxation in complex viscoelastic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 449-453.
    6. Tan, Hailian & Wu, Jianwei & Bao, Haibo, 2022. "Event-triggered impulsive synchronization of fractional-order coupled neural networks," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    7. Shafiya, M. & Nagamani, G. & Dafik, D., 2022. "Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 168-186.
    8. 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).
    9. Hou, Mimi & Xi, Xuan-Xuan & Zhou, Xian-Feng, 2021. "Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    10. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
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