Continuum limit of self-driven particles with orientation interaction
Mathematical Physics
2014-04-08 v1 math.MP
Abstract
We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, 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 and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.
Cite
@article{arxiv.0710.0293,
title = {Continuum limit of self-driven particles with orientation interaction},
author = {Pierre Degond and Sébastien Motsch},
journal= {arXiv preprint arXiv:0710.0293},
year = {2014}
}