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Exponential stability of complex-valued memristor-based neural networks with time-varying delays

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  • Shi, Yanchao
  • Cao, Jinde
  • Chen, Guanrong

Abstract

In this paper, we propose a new type of complex-valued memristor-based neural networks with time-varying delays and discuss their exponential stability. Firstly, by using a matrix measure method, the Halanay inequality and some analytic techniques, we derive a sufficient condition for the global exponential stability of this type of neural networks. Then, we build a Lyapunov functional and utilize the Halanay inequality to establish several criteria for the exponential stability of such networks with time-varying delays. Finally, we show two numerical simulations to demonstrate the theoretical results.

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  • Shi, Yanchao & Cao, Jinde & Chen, Guanrong, 2017. "Exponential stability of complex-valued memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 222-234.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:222-234
    DOI: 10.1016/j.amc.2017.05.078
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    5. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
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    Cited by:

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    5. Li, Ruoxia & Cao, Jinde & Xue, Changfeng & Manivannan, R., 2021. "Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. 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.
    7. Wang, Lingyu & Huang, Tingwen & Xiao, Qiang, 2018. "Global exponential synchronization of nonautonomous recurrent neural networks with time delays on time scales," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 263-275.
    8. Yao, Xueqi & Zhong, Shouming & Hu, Taotao & Cheng, Hong & Zhang, Dian, 2019. "Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 392-403.
    9. Cheng, Lin & Yang, Yongqing & Li, Li & Sui, Xin, 2018. "Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 273-286.
    10. Sriraman, R. & Cao, Yang & Samidurai, R., 2020. "Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 103-118.
    11. Luo, Yiping & Deng, Fei & Ling, Zhaomin & Cheng, Zifeng, 2019. "Local H∞ synchronization of uncertain complex networks via non-fragile state feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 335-346.
    12. Pu, Hao & Li, Fengjun, 2023. "Fixed/predefined-time synchronization of complex-valued discontinuous delayed neural networks via non-chattering and saturation control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    13. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    14. Cao, Yang & Sriraman, R. & Shyamsundarraj, N. & Samidurai, R., 2020. "Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 207-220.
    15. Yang, Ni & Gao, Ruiyi & Su, Huan, 2022. "Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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