We study emergent dynamics of the discrete Cucker–Smale (in short, DCS) model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient framework is formulated in terms of an admissible set of network topologies realized by digraphs and probability density function for random switching times. As examples for the law of switching times, we use the Poisson process and the geometric process and show that these two processes satisfy the required conditions in a given framework so that we have a stochastic flocking with probability one. As a corollary of our flocking analysis, we improve the earlier result [J.-G. Dong, S.-Y. Ha, J. Jung, and D. Kim, SIAM J. Control Optim., 58(4):2332–2353, 2019] on the continuous CS model.

中文翻译：

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具有随机切换拓扑的离散Cucker-Smale模型的随机植绒的出现

我们研究具有随机切换网络拓扑的离散Cucker-Smale模型（简称DCS）的动态模型。为此，我们提供了一个足够的框架来导致随机植绒的可能性为一。我们的充分框架是根据有向图和概率密度函数针对随机切换时间实现的一组可允许的网络拓扑结构制定的。作为切换时间定律的示例，我们使用了泊松过程和几何过程，并证明这两个过程在给定的框架内满足要求的条件，因此我们具有概率为1的随机植绒。作为植绒分析的必然结果，我们改进了早期的结果[J.-G. 董善玉 Ha，J. Jung和D. Kim，SIAM J. Control Optim。，58（4）：2332–2353，2019]。