A Model of Self-Propelled Particles Coordinating Under External Leadership

In this paper, we investigate the emergence of organization patterns in a group of self-propelled particles in the presence of a mobile external leader particle. Particle-to-particle interactions and particle-to-leader interactions are described through biologically-relevant pairwise potentials. Simulation results in two dimensions reveal the existence of a variety of long run particle aggregation states, including highly polarized tracking of the leader and coherent milling about it. Transition between aggregation states is triggered by the interplay of particle energy, group size, interaction strength, and leader mobility. These findings provide insights in the structure and organization of biological groups under the influence of external aggregation devices, environmental stimuli, or trained individuals taking the lead.