Obstacle and predator avoidance by a flock

Abstract

The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this paper, we present a continuum model of flocking and use it to investigate the reaction of a flock to an obstacle or an attacking predator. We show that the 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.

24 pages, 9 figures

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• Continuum modeling of the equilibrium and stability of animal flocks
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• Control to flocking of the kinetic Cucker-Smale model