  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.
