Abstract

Collective migration of cells and animals often relies on a specialised set of “leaders”, whose role is to steer a population of naive followers towards some target. We investigate the dynamics and structure of such groups using a continuous approach where a population is subdivided into follower and leader types with non-local interactions and different orientation responses influencing the turning rates of group members. Within this modeling framework, we formulate different alignment interaction terms describing different degrees of leadership ranging from (i) distinct leadership, where leaders have absolute knowledge of the target and followers have none, to (ii) subtle leadership, where leaders are partially informed and leaders and followers have less clear differences in their behaviour. In each resulting model, we incorporate leader influence via three mechanisms: a bias in the orientation of leaders towards the destination (orientation-bias), a faster movement of leaders when moving towards the target (speed-bias), and leaders making themselves more clear to followers when moving towards the target (conspicuousness-bias). Analysis and numerical computation are used to illustrate the various patterns displayed by the models, thus assessing the extent to which the swarm is successfully shepherded towards the destination.