Synchronization of individual heading deviations in finite flocks of self-propelled Vicsek particles

Abstract

In flocking birds, swarming bacteria, and many other real-world systems, the individual departures from a group's global behavior are the usual triggers of spontaneous collective directional switching. In this study, we revisit the Vicsek model for collective motion and investigate the degree of phase and amplitude synchronization of individual heading deviations from the flock's global direction, i.e., by employing the Kuramoto order parameter and the mutual information metric as phase and amplitude synchronization quantifiers, respectively. Through numerical simulations of Vicsek systems at fixed particle speed and density but varying noise intensities, we find that the synchronization of phases and amplitudes of individual heading deviations are independent of each other. Also, we observe that as the noise intensity is decreased, the amplitudes of these individual heading deviations tend to diverge despite their phases being synchronized.