论文标题
模糊$ q $ - closest对准模型
A fuzzy $q$-closest alignment model
论文作者
论文摘要
该论文研究了与cucker-smale模型相关的问题，其通信仅限于$ q $ closest邻居，也称为cucker-dong模型。随着代理在不同簇的边界上振荡，系统很难精确定义，这会导致动力学限制的进一步问题，因为代理的数量倾向于无穷大。我们介绍了模糊$ Q $ -Closest System，该系统以良好的态度规避了问题。对于这样的系统，我们证明了测量值解决方案的稳定性估计值并执行动力学平均场极限。
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the $q$-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy $q$-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.
