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Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise

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  • Yu, Peilin
  • Deng, Feiqi
  • Sun, Yuanyuan
  • Wan, Fangzhe

Abstract

This note investigates the stabilities for impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise (ISDCGNNs-LN), including the input-to-state stability (ISS), integral input-to-state stability (iISS) and ϕθ(t)-weight input-to-state stability (ϕθ(t)-weight ISS, θ>0). Utilizing the multiple Lyapunov-Krasovskii (L-K) functions, principle of comparison, constant variation method and average impulsive interval (AII) method, adequate ISS-type stability conditions of the ISDCGNNs-LN under stable impulse and unstable impulse are obtained. This shows that the stochastic systems are ISS in regard to a lower bound of the AII, provided that the continuous stochastic systems is ISS but has destabilizing impulse. Furthermore, the impulse can effectively stabilize the stochastic systems for a upper bound of the AII, provided that the continuous stochastic systems is not ISS. In addition, our results can also deal with the case of variable time delay. In the end, two examples are presented to reflect the rationality and correctness for the theoretical conclusions.

Suggested Citation

  • Yu, Peilin & Deng, Feiqi & Sun, Yuanyuan & Wan, Fangzhe, 2022. "Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005185
    DOI: 10.1016/j.amc.2022.127444
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    References listed on IDEAS

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    1. Fu, Xiaozheng & Zhu, Quanxin, 2020. "Exponential stability of neutral stochastic delay differential equation with delay-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Kolasa, Marta & Talaska, Tomasz & Długosz, Rafał, 2015. "A novel recursive algorithm used to model hardware programmable neighborhood mechanism of self-organizing neural networks," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 314-328.
    3. Jin, Zhenghong & Wang, Zhanxiu, 2021. "Input-to-state stability of the nonlinear singular systems via small-gain theorem," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. Fu, Teng & Zhou, Yusheng, 2022. "Stabilization of switched time-delay systems with only unstable subsystems: a new approach based on a vibration model of 1.5 degrees of freedom," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    5. You, Surong & Mao, Wei & Mao, Xuerong & Hu, Liangjian, 2015. "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 73-83.
    6. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    7. Zhu, Xingao & Liu, Shutang, 2022. "Reachable set estimation for continuous-time impulsive switched nonlinear time-varying systems with delay and disturbance," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    Full references (including those not matched with items on IDEAS)

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