Continuum limit of self-driven particles with orientation interaction

被引：274

作者：

Degond, Pierre ^{[1
]}

Motsch, Sebastien ^{[1
]}

机构：

[1] Univ Toulouse 3, CNRS UPS INSA UT1 UT2, UMR 5219, Inst Math, F-31062 Toulouse, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2008年 / 18卷 / SUPPL.期

关键词：

individual based model; fish behavior; Couzin-Vicsek algorithm; asymptotic analysis; orientation interaction; hydrodynamic limit; collision invariants;

D O I：

10.1142/S0218202508003005

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

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.

引用

页码：1193 / 1215

页数：23

共 37 条

[1]

Phase transitions in self-driven many-particle systems and related non-equilibrium models: A network approach [J].

Aldana, M ;

Huepe, C .

JOURNAL OF STATISTICAL PHYSICS, 2003, 112 (1-2) :135-153

[2]

[Anonymous], SELF ORG BIOL SYSTEM

[3]

AOKI I, 1982, B JPN SOC SCI FISH, V48, P1081

[4]

A model for the dynamics of large queuing networks and supply chains [J].

Armbruster, D ;

Degond, P ;

Ringhofer, C .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (03) :896-920

[5]

Derivation of continuum traffic flow models from microscopic follow-the-leader models [J].

Aw, A ;

Klar, A ;

Materne, T ;

Rascle, M .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 63 (01) :259-278

[6]

Employing stochastic differential equations to model wildlife motion [J].

Brillinger, DR ;

Preisler, HK ;

Ager, AA ;

Kie, JG ;

Stewart, BS .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2002, 33 (03) :385-408

[7]

THE FLUID DYNAMIC LIMIT OF THE NON-LINEAR BOLTZMANN-EQUATION [J].

CAFLISCH, RE .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (05) :651-666

[8]

CERCIGNANI C, 1991, MATH THEORY DILUTE G

[9]

State transitions and the continuum limit for a 2D interacting, self-propelled particle system [J].

Chuang, Yao-Li ;

D'Orsogna, Maria R. ;

Marthaler, Daniel ;

Bertozzi, Andrea L. ;

Chayes, Lincoln S. .

PHYSICA D-NONLINEAR PHENOMENA, 2007, 232 (01) :33-47

[10]

Collective memory and spatial sorting in animal groups [J].

Couzin, ID ;

Krause, J ;

James, R ;

Ruxton, GD ;

Franks, NR .

JOURNAL OF THEORETICAL BIOLOGY, 2002, 218 (01) :1-11

← 1 2 3 4 →