一类具有切换拓扑和随机故障影响的集群演化模型分析  

Flocking Behaviour Analysis for a Collective Model with Switching Topologies and Random Failure Effects

作　　者：乔正阳 刘易成[1] QIAO Zhengyang;LIU Yicheng(Department of Mathematics,National University of Defense Technology,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1期146-157,共12页Mathematica Applicata

基　　金：国家自然科学基金(11671011,11428101)。

摘　　要：本文研究带有切换拓扑和随机故障影响的Cucker-Smale模型的集群演化特点,在切换时间间隔和故障概率满足一定约束条件下,给出系统几乎必然发生集群演化的充分条件.鉴于随机故障和拓扑切换的综合影响,Cucker-Smale模型产生了复杂的集群演化行为,其中集群收敛速度随着故障概率的增加会显著减慢.同时,我们在切换过程中并不要求每时每刻的交互图都具生成树.只需保证在有限时间段内联合图具有生成树.进一步,数值仿真结果显示,当切换时间间隔增加或故障概率较大时,系统的集群演化行为将会遭到破坏.In this paper,we investigate the flocking evolution behaviours of the Cucker-Smale model with switching topologies and random failure effects.Under certain constraints of switching interval and failure probability,we give sufficient conditions for the flocking evolution of the system.Considering the combined effects,we find the complex flocking evolution behavior for the modified Cucker-Smale model,in which the flocking convergent speed slows down as failure probability increasing.Meanwhile,we don’t limit the existence of spanning tree for each interaction graph in the process of switching,and only the joint graph has spanning trees in a limited interval.Furthermore,numerical simulation results show that when the switching time interval increases or the failure probability is large,the flocking evolution behavior of the system will be destroyed.

关 键 词：集群 随机故障 切换拓扑 生成树 

分 类 号：O175[理学—数学]