We investigate the stability of Boolean networks (BNs) with impulses triggered by both states and random factors. A hybrid index model is used to describe impulsive BNs. First, several necessary and sufficient conditions for forward completeness are obtained. Second, based on the stability criterion of probabilistic BNs and the forward completeness criterion, the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented. The relationship between these two kinds of stability is discussed. Last, examples and time-domain simulations are provided to illustrate the obtained results.

中文翻译：

---

具有状态相关随机脉冲的布尔网络的稳定性

我们调查布尔网络（BNs）的状态和随机因素触发的脉冲的稳定性。混合索引模型用于描述脉冲BN。首先，获得若干必要条件和充分条件以保证前向完整性。其次，基于概率BNs的稳定性准则和前向完整性准则，给出了概率为1的有限时间稳定性和分布的渐近稳定性的充要条件。讨论了这两种稳定性之间的关系。最后，提供了示例和时域仿真来说明获得的结果。