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.
L'algorithme discret de Couzin–Vicsek (CVA) a été proposé pour modéliser l'interaction d'individus au sein de sociétés animales comme les bancs de poissons. Dans cette Note, nous proposons une version cinétique (champ-moyen) de l'algorithme CVA et en donnons la limite macroscopique formelle. Le modèle macroscopique final comprend une équation de conservation pour la densité des individus et une équation non-conservative pour le vecteur directeur de la vitesse moyenne. Ce résultat est basé sur l'introduction d'un concept non-conventionnel d'invariant collisionnel de l'opérateur de collision.
Accepted:
Published online:
Pierre Degond 1; Sébastien Motsch 1
@article{CRMATH_2007__345_10_555_0,
author = {Pierre Degond and S\'ebastien Motsch},
title = {Macroscopic limit of self-driven particles with orientation interaction},
journal = {Comptes Rendus. Math\'ematique},
pages = {555--560},
publisher = {Elsevier},
volume = {345},
number = {10},
year = {2007},
doi = {10.1016/j.crma.2007.10.024},
language = {en},
}
Pierre Degond; Sébastien Motsch. Macroscopic limit of self-driven particles with orientation interaction. Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 555-560. doi : 10.1016/j.crma.2007.10.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.024/
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