Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions  

作　　者：Chun Yin JIN Shuang Zhi LI 

机构地区：[1]College of Science,China Agricultural University,Beijing 100083,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第9期2285-2296,共12页数学学报（英文版）

基　　金：The first author is supported by NSFC(Grant No.12001530)。

摘　　要：How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory.Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance(cf.Motsch and Tadmor in J.Stat.Phys.2011).In this paper,we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions.Using properties of a connected stochastic matrix,together with an elaborate analysis on perturbations of a linearized system,we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking.Moreover,it is shown that the system achieves flocking at an exponential rate.

关 键 词：Cucker-Smale model local interaction FLOCKING stochastic matrix neighbor graph 

分 类 号：O231[理学—运筹学与控制论]