Obstacle and predator avoidance in a model for flocking

The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this paper, we present a deterministic continuum model of flocking and use it to investigate the linearized response of an infinite extent flock to an obstacle or an attacking predator. We show that the steady-state flock response is in the form of density disturbances that resemble Mach cones whose configuration is determined by the anisotropic propagation of waves through the flock. We analytically and numerically test relations that predict the Mach wedge angles, disturbance heights, and wake widths. We find that these expressions are insensitive to many of the parameters of the model.