具斥力函数的奇异Cucker-Smale模型的渐近免碰撞集群

Asymptotic Collision-avoidance Flocking of Singular Cucker-Smale Models with Repulsion Functions

针对一个改进的Cucker-Samle模型的免碰撞问题,利用奇异权函数与排斥力结合的方法,证明了当排斥力函数中的幂指数m∈[1,2)时只要系统中的粒子在初始时刻不发生碰撞,系统的集群会无条件发生且粒子不会发生碰撞.最后数值模拟进一步验证理论结论正确性。

This paper considers, we consider the method of combining singular weight function with repulsive force for an improved Cucker-Samle model’s collision-avoidance problem, and prove that when the power of the repulsive force function m∈[1,2), as long as the particles in the system do not collide at the initial moment, the flocking of the system will occur unconditionally and the particles will not collide. Finally, numerical simulation further verifies the correctness of the theoretical conclusion.