Hegselmann-Krause模型的稀疏控制：黑洞与去聚
Sparse control of Hegselmann-Krause models: Black hole and declustering
摘要：
本文阐述了控制策略，以防止集群效应的意见形成模型。这与文献中遇到的许多情况完全相反，相反，人们寻求促进共识的控制。为了促进去聚类，而不是使用经典的方差，不能很好地捕捉分散的现象，我们引入了一个熵型功能，适用于测量代理之间的成对距离。然后，我们专注于一个Hegselmann-Krause型系统和设计分散稀疏控制在有限维和动力学模型。我们提供了一般的条件，表征聚类是否可以避免作为初始数据的函数。这些结果包括黑洞的描述（完全崩溃到共识是不可避免的），安全区（控制可以使系统远离聚类），吸引盆地（聚类集周围的吸引区）和崩溃预防（当可以避免收敛到聚类集时）。
英文摘要：
This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting consensus. In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, we introduce an entropy-type functional that is adapted to measuring pairwise distances between agents. We then focus on a Hegselmann-Krause-type system and design declustering sparse controls both in finite-dimensional and kinetic models. We provide general conditions characterizing whether clustering can be avoided as function of the initial data. Such results include the description of black holes (where complete collapse to consensus is not avoidable), safety zones (where the control can keep the system far from clustering), basins of attraction (attractive zones around the clustering set) and collapse prevention (when convergence to the clustering set can be avoided).
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。
