Collective queuing motion of self-propelled particles with leadership and experience

The coordinated and ordered collective behavior arising from dispersed and local self-organizing interactions among individuals is widely observed in many biological communities. For populations engaging in group foraging or migration, complex societies with multiple hierarchical levels are common. A prevalent scenario involves two dominant levels, one corresponding to leaders and the other composed of followers. In this paper, we explore how a group can be influenced by a set of leaders to organize and move in a coordinated manner towards a preferred direction. Specifically, we balance social interactions among group members through two weighted factors, corresponding to the leadership and experience of leaders. Through computer simulations, we observe a linear relationship between the proportion of leaders guiding group movement and the group size, with larger groups requiring a higher proportion of leaders while maintaining initial density. Additionally, we identify an optimal leadership interval where group movement performance enhances with increasing leadership up to a certain point, beyond which it starts to decline. Similar patterns are observed concerning individual visual field, indicating the existence of an optimal interval for visual angle. Our findings not only contribute to understanding collective motion in natural biological systems but also provide new insights into effective leadership mechanisms in artificial swarm systems.