Collective motion of a finite sized flock: I know why the caged bird flocks

Abstract

The Vicsek model offers a phenomonologically rich set of behaviours while maintaining simple rules of interaction. By introducing a convex hull as a means of providing cohesion within the system, we have been able to probe the behaviour of this model as it is moved off of the usual periodic boundary conditions, to the infinite plane. We present the findings of 4 different schemes that introduce this cohesive effect by way of deflecting Boids on the convex hull back into the bulk. In one such scheme, a new phase transition is found, between a state wherein the flock has a constant direction of motion, and a state where this direction precesses. The rate of precession is found to be dependent on both the noise level and the deflection coupling.