2007/10/01 by Pierre Degond, PIERRE DEGOND, Sébastien Motsch +1 · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #msc:35L60 #msc:35Q80 #msc:82C22 #msc:82C70 #msc:92D50
paper · pdf · doi:10.1142/s0218202508003005
published as Mathematical Models and Methods in Applied Sciences 18, Suppl. (2008), pp. 1193-1215
arxiv created 2007/10/01 · crossref issued 2008/08/01 · crossref published 2008/08/01 · crossref published-print 2008/08/01 · crossref created 2008/08/06 · crossref published-online 2011/11/21 · arxiv updated 2014/04/08 · crossref deposited 2024/03/25 · crossref indexed 2026/08/06
The discrete Couzin–Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools is considered. In this paper, a kinetic (mean-field) version of the CVA model is proposed and its formal macroscopic limit is provided. 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.