Vicsek Model Meets DBSCAN: Cluster Phases in the Vicsek Model

Abstract

The Vicsek model, which was originally proposed to explain the dynamics of bird flocking, exhibits a phase transition with respect to the absolute value of the mean velocity. Although clusters of agents can be easily observed via numerical simulations of the Vicsek model, qualitative studies are lacking. We study the clustering structure of the Vicsek model by applying DBSCAN, a recently-introduced clustering algorithm, and report that the Vicsek model shows a phase transition with respect to the number of clusters: from O(N) to O(1), with N being the number of agents, when increasing the magnitude of noise for a fixed radius that specifies the interaction of the Vicsek model. We also report that the combination of the order parameter proposed by Vicsek et al. and the number of clusters defines at least four phases of the Vicsek model.