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Cucker-Smale flocking with alternating leaders

We study the emergent flocking behavior in a group of Cucker-Smale flocking agents under rooted leadership with alternating leaders. It is well known that the network topology regulates the emergent behaviors of flocks. All existing results on the Cucker-Smale model with leader-follower topologies assume a fixed leader during temporal evolution process. The rooted leadership is the most general topology taking a leadership. Motivated by collective behaviors observed in the flocks of birds, swarming fishes and potential engineering applications, we consider the rooted leadership with alternating leaders; that is, at each time slice there is a leader but it can be switched among the agents from time to time. We will provide several sufficient conditions leading to the asymptotic flocking among the Cucker-Smale agents under rooted leadership with alternating leaders.