Macroscopic limit of self-driven particles with orientation interaction
Pierre Degond, Sébastien Motsch · Comptes Rendus Mathématique · 2007
The discrete Couzin–Vicsek algorithm (CVA) has been proposed to model the interactions of individuals among animal societies such as schools of fish. In this Note, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity. The result is based on the introduction of a non-conventional concept of a collisional invariant of the collision operator.