Consensus decision-making of animal groups in motion

In this paper, we will investigate the effectiveness of leaders in animal groups by a discrete-time multi-agent system. The model is composed of two subgroups of agents: informed agents(called leaders) and uninformed agents(called followers). All agents move in the plane with a constant speed, but with different heading update laws. For the followers, the heading is updated according to the average direction of neighbors, while the heading of leaders is taken as the balance between the local interaction of neighbors and the preferred direction. For such a system, we will provide a necessary condition and a sufficient condition for the consensus decision-making.