等级领导与随机互动下的Cucker-Smale群集行为
Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions
摘要：
考虑一群鸟在它们之间相互作用。的相互作用是通过一个分层系统中，每只鸟，在每个时间步，调整自己的速度，根据他过去的速度和加权平均值的相对速度的上级在层次结构中。我们考虑另外一个事实，即每只鸟都有一定的概率看不到它的上级，这取决于它们之间的距离。对于这个模型的随机相互作用，我们证明了群集现象，获得类似的确定性模型，持有真实的。
英文摘要：
Consider a flock of birds that fly interacting between them. The interactions are modelled through a hierarchical system in which each bird, at each time step, adjusts its own velocity according to his past velocity and a weighted mean of the relative velocities of its superiors in the hierarchy. We consider the additional fact, that each of the birds can fail to see any of its superiors with certain probability, that can depend on the distances between them. For this model with random interactions we prove that the flocking phenomena, obtained for similar deterministic models, holds true.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
