  The features of animal population dynamics, for instance, flocking and
migration, are often synchronized for survival under large-scale climate change
or perceived threats. These coherent phenomena have been explained using
synchronization models. However, such models do not take into account
asynchronous and adaptive updating of an individual's status at each time.
Here, we modify the Kuramoto model slightly by classifying oscillators as
leaders or followers, according to their angular velocity at each time, where
individuals interact asymmetrically according to their leader/follower status.
As the angular velocities of the oscillators are updated, the leader and
follower status may also be reassigned. Owing to this adaptive dynamics,
oscillators may cooperate by taking turns acting as a leader or follower. This
may result in intriguing patterns of synchronization transitions, including
hybrid phase transitions, and produce the leader-follower switching pattern
observed in bird migration patterns.
