Continuum limit of self-driven particles with orientation interaction

Pierre Degond; Sébastien Motsch

doi:10.1142/S0218202508003005

Continuum limit of self-driven particles with orientation interaction

Pierre Degond, Sébastien Motsch

Research output: Contribution to journal › Article › peer-review

264 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	1193-1215
Number of pages	23
Journal	Mathematical Models and Methods in Applied Sciences
Volume	18
Issue number	SUPPL.
DOIs	https://doi.org/10.1142/S0218202508003005
State	Published - Aug 2008
Externally published	Yes

Keywords

Asymptotic analysis
Collision invariants
Couzin-Vicsek algorithm
Fish behavior
Hydrodynamic limit
Individual based model
Orientation interaction

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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10.1142/S0218202508003005

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title = "Continuum limit of self-driven particles with orientation interaction",

abstract = "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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author = "Pierre Degond and S{\'e}bastien Motsch",

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language = "English (US)",

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AU - Motsch, Sébastien

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AB - 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.

KW - Asymptotic analysis

KW - Collision invariants

KW - Couzin-Vicsek algorithm

KW - Fish behavior

KW - Hydrodynamic limit

KW - Individual based model

KW - Orientation interaction

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ER -

Continuum limit of self-driven particles with orientation interaction

Abstract

Keywords

ASJC Scopus subject areas

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