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Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances

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  • Liu, Shuxin
  • Yu, Yongguang
  • Zhang, Shuo
  • Zhang, Yuting

Abstract

The robust stability of fractional-order memristor-based Hopfield neural networks (FMHNNs) with parameter disturbances is addressed in this paper. Based on the fractional-order Lyapunov direct method, some sufficient conditions on the robust stability are established. For such neural system with discontinuous right-hand sides, its existence and uniqueness of the equilibrium point are analyzed in the Filippov sense and the robust stability is also achieved. Finally, the numerical example is given to show the effectiveness of the proposed method.

Suggested Citation

  • Liu, Shuxin & Yu, Yongguang & Zhang, Shuo & Zhang, Yuting, 2018. "Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 845-854.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:845-854
    DOI: 10.1016/j.physa.2018.06.048
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    References listed on IDEAS

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    1. Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Hui Zhao, 2016. "Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(9), pages 1-11, September.
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    4. Huaiqin Wu & Luying Zhang & Sanbo Ding & Xueqing Guo & Lingling Wang, 2013. "Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
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    Cited by:

    1. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Xu, Wei & Zhu, Song & Fang, Xiaoyu & Wang, Wei, 2019. "Adaptive anti-synchronization of memristor-based complex-valued neural networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    4. He, Jin-Man & Pei, Li-Jun, 2023. "Function matrix projection synchronization for the multi-time delayed fractional order memristor-based neural networks with parameter uncertainty," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    5. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    6. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    7. Yao, Xueqi & Zhong, Shouming, 2021. "EID-based robust stabilization for delayed fractional-order nonlinear uncertain system with application in memristive neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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