一类非对称Cucker-Smale模型的直线型编队  

Linear Formation for a Cucker-Smale Model with Asymmetric Influence

作　　者：吴俊滔 陈茂黎 王晓[1] WU JUNTAO;CHEN MAOLI;WANG XIAO(College of Liberal Arts and Sciences,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学文理学院,长沙410073

出　　处：《应用数学学报》2020年第6期966-983,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11671011)资助项目。

摘　　要：针对具有两部分粒子簇数目悬殊较大的多粒子群的聚集与直线编队问题,研究了一类具有非对称影响函数和直线编队驱动力的Cucker-Smale模型的动力学行为.通过构造能力函数,建立微分不等式和原系统的投影系统等方法,获得了此类多粒子群同时形成集群与直线编队的充分条件.研究结果表明,在集群条件下,多粒子群能够形成集群并在预设的任意方向上实现直线编队,数值仿真进一步验证了研究结果的正确性.Aiming at the problem of the aggregation and linear formation of multi-particle swarms with a large disparity between two clusters of particles,dynamical behavior for a class of Cucker-Smale model with asymmetric influence function and driving force of linear formation is investigated.Based on the the energy function method,some differential inequalities and the relationship between the original system and its projection system,sufficient conditions are constructed for the simultaneous implementation of a time-asymptotic flocking and linear formation are established.The results show that under the flocking conditions,the multi-particle group can converge asymptotically to form a flock and form a straight line formation in a predetermined arbitrary direction.Finally,numerical simulation results are given to verify the validity of the theoretical analysis.

关 键 词：非对称影响 直线编队 时间渐近集群 

分 类 号：O193[理学—数学]