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Globally β-Mittag-Leffler stability and β-Mittag-Leffler convergence in Lagrange sense for impulsive fractional-order complex-valued neural networks

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  • Li, Hui
  • Kao, Yonggui
  • Li, Hong-Li

Abstract

This paper explores the globally β-Mittag-Leffler stability in Lagrange sense for the fractional-order complex-valued neural network (FOCVNN) with impulsive effects. By Lyapunov method and matrix inequalities, some novel sufficient conditions are obtained to guarantee the globally β-Mittag-Leffler stability in Lagrange sense for two class of complex-valued (CV) activation functions. The convergent rate is also given, which is controlled by the parameters of the addressed system. The existence and uniqueness of the solution for this system do not require consideration. To show the validity and usefulness of the results, two numerical stimulations are provided.

Suggested Citation

  • Li, Hui & Kao, Yonggui & Li, Hong-Li, 2021. "Globally β-Mittag-Leffler stability and β-Mittag-Leffler convergence in Lagrange sense for impulsive fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s096007792100415x
    DOI: 10.1016/j.chaos.2021.111061
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    References listed on IDEAS

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    1. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
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    5. Li, Hui & Kao, YongGui, 2019. "Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 22-31.
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    7. 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.
    8. R. Saravanakumar & M. Syed Ali & Jinde Cao & He Huang, 2016. "state estimation of generalised neural networks with interval time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(16), pages 3888-3899, December.
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    Cited by:

    1. Jianying Xiao & Yongtao Li, 2022. "Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    2. Yang, Zhanwen & Li, Qi & Yao, Zichen, 2023. "A stability analysis for multi-term fractional delay differential equations with higher order," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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