期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 18, 期 -, 页码 1193-1215出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202508003005
关键词
individual based model; fish behavior; Couzin-Vicsek algorithm; asymptotic analysis; orientation interaction; hydrodynamic limit; collision invariants
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.
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