Emergence of leadership in complex networks and human groups

Leadership is a complex yet fascinating phenomenon crucial in many application where coordination of multi-agent systems is involved. This is particularly true in the case of animal groups and other natural systems including human ensembles where, for example in orchestras, a leader is often selected to steer the group towards some desired coordinated behaviour. In this paper we study the emergence of leadership in networks of heterogeneous Kuramoto oscillators, which offer a good model for capturing and describing coordination in human groups performing a joint oscillatory task. We present a mathematical framework to establish phase leadership in the network and apply the results to inform some preliminary experimental results in human groups.