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Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion

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  • Ren, Yong
  • He, Qian
  • Gu, Yuanfang
  • Sakthivel, R.

Abstract

This paper studies the mean-square exponential input-to-state stability for a class of delayed impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. By constructing an appropriate G-Lyapunov–Krasovskii functional, mathematical induction approach and some inequality techniques, a new set of sufficient conditions is obtained for the mean-square exponential input-to-state stability of the trivial solutions for the considered systems. Finally, an example is given to illustrate the obtained theory.

Suggested Citation

  • Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.
    • Handle: RePEc:eee:stapro:v:143:y:2018:i:c:p:56-66
    DOI: 10.1016/j.spl.2018.07.024
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    References listed on IDEAS

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    1. R. Sakthivel & R. Samidurai & S. M. Anthoni, 2010. "Asymptotic Stability of Stochastic Delayed Recurrent Neural Networks with Impulsive Effects," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 583-596, December.
    2. Ren, Yong & Hu, Lanying, 2011. "A note on the stochastic differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 580-585, May.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    4. Raja, R. & Zhu, Quanxin & Senthilraj, S. & Samidurai, R., 2015. "Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1050-1069.
    5. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    6. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
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    Cited by:

    1. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Leelamani, A., 2020. "Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Yin, Wensheng & Cao, Jinde, 2021. "On stability of large-scale G-SDEs: A decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    3. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.

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