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 ${\varphi }^{\theta }\left(t\right)$-weight input-to-state stability (${\varphi }^{\theta }\left(t\right)$-weight ISS, $\theta >0$). 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.

本笔记研究了由 Lévy 噪声 (ISDCGNNs-LN) 驱动的脉冲随机延迟 Cohen-Grossberg 神经网络的稳定性，包括输入到状态稳定性 (ISS)、积分输入到状态稳定性 (iISS) 和${\phi }^{\theta }\left(吨\right)$-权重输入到状态稳定性（${\phi }^{\theta }\left(吨\right)$-重量国际空间站，$\theta >0$）。利用多重Lyapunov-Krasovskii(LK)函数、比较原理、常数变化法和平均脉冲间隔(AII)法，得到了ISDCGNNs-LN在稳定脉冲和不稳定脉冲下足够的ISS型稳定性条件。这表明随机系统是关于 AII 下界的 ISS，前提是连续随机系统是 ISS 但具有不稳定的冲量。此外，如果连续随机系统不是 ISS，则脉冲可以有效地稳定 AII 上限的随机系统。此外，我们的结果还可以处理可变时间延迟的情况。最后通过两个例子来反映理论结论的合理性和正确性。