Multi-cluster flocking behavior of the hierarchical Cucker-Smale model

In this paper, we investigate the multi-cluster flocking behavior of the hierarchical Cucker-Smale model parameterized by a constant beta measuring the strength of the interaction between agents. The previous studies showed that when 0 <=beta<1/2 unconditional flocking would occur, while for beta >= 1/2 conditional flocking would occur provided the initial data satisfy some given conditions. We will show in this paper that, when beta =1/2, unconditional flocking would occur for the model, while for beta> 1/2, we give a complete understanding for the asymptotic multi-cluster formation when the initial positions and velocities have the ordering relations: by computing the initial data we can specify how many clusters emerge and which agents are in the same cluster. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.