On non-collision flocking and line-shaped spatial configuration for a modified singular Cucker-Smale model

摘要

This paper is concerned with a singular Cucker-Smale model with a general targeted pattern driving force, which ensures that the particles finally come to the desired spatial configuration. Under some suitable conditions, we prove that the exponent alpha = 1 in the communication weight leads to global regularity of solutions so that the system has an asymptotic flocking without collision between any agent. As an example, a prescribed driving force is given to demonstrate that the particles finally come to a line-shaped formation with collision avoidance, which can be viewed as a reasonable explanation for the wild geese flying in a line-shape in the sky. Moreover, this mechanism can be applied to the UAVs forming a line-shape to complete some special military missions. These results are novel, which are illustrated by both theoretical analysis and numerical simulations. (C) 2019 Published by Elsevier B.V.