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arXiv · 0710.0293

Continuum limit of self-driven particles with orientation interaction

Pierre Degond·Sébastien Motsch
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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.

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Pierre Degond, Sébastien Motsch. 2007-10-01. Continuum limit of self-driven particles with orientation interaction. https://doi.org/10.1142/s0218202508003005

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