一类混合型Cucker-Smale模型的有限时间集群  

Finite-time Flocking of a Kind of Mixed Cucker-Smale Model

作　　者：吴俊滔 王晓[1] 刘易成[1] WU Juntao;WANG Xiao;LIU Yicheng(Department of Mathematics,National University of Defense Technologu,Changsha 410073,China)

机构地区：[1]国防科技大学数学系,湖南长沙410073

出　　处：《应用数学》2021年第3期711-724,共14页Mathematica Applicata

基　　金：国家自然科学基金(11671011)。

摘　　要：本文研究一类带有非Lipschitz连续项与Lipschitz连续项混合型的CuckerSmale模型的有限时间集群问题.基于能量函数方法与微分不等式,通过从交流函数、位移、速度标准差等方面对系统有限时间集群的形成进行分析,构建了此类多粒子群有限时间形成集群的充分条件,此结果去掉了有限时间集群对交流函数具有正的下界的要求.进一步地,结果表明,在一定条件下,该系统的有限时间集群行为主要由非Lipschitz连续项决定,数值仿真进一步验证结果的正确性.This paper studies a class of finite-time flocking problems of the Cucker-Smale model with a mixture of non-Lipschitz and Lipschitz continuous terms.Based on the energy function method and differential inequality,the system is analyzed from the aspects of interactive function,displacement,speed standard deviation,etc.The formation of finite-time flocks was analyzed,and the sufficient conditions for forming such multi-particle swarms to form flocks in finite time were constructed.This result removes the requirement that the finite-time flocks have a positive lower bound on the interactive function.Further,the results show that under certain conditions,the finite-time flock behavior of this system is mainly determined by non-Lipschitz continuous terms,and numerical simulation further verifies the correctness of the results.

关 键 词：Cucker-Smale模型 LIPSCHITZ连续 有限时间集群 

分 类 号：O193[理学—数学]