Time periodic flocking phenomena

Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic trend, the result may be a periodic adjustment of the flock. This is demonstrated by analyzing a modified Vicsek model of self-propelled particles and its corresponding Ihle-Enskog kinetic equation valid in the limit of infinitely many particles. We have carried out a stability and bifurcation analysis of the order-disorder transition to a time periodic solution characterized by a new order parameter. Direct numerical simulations confirm the theoretical findings.