EMERGENCE OF MULTI-CLUSTER CONFIGURATIONS FROM ATTRACTIVE AND REPULSIVE INTERACTIONS

被引：21

作者：

Ha, Seung-Yeal ^{[1
]}

Jeong, Eunhee ^{[1
]}

Kang, Jeong-Han ^{[2
]}

Kang, Kyungkeun ^{[3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Yeonsei Univ, Dept Sociol, Seoul 120749, South Korea

[3] Yeonsei Univ, Dept Math, Seoul 120749, South Korea

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2012年 / 22卷 / 08期

基金：

新加坡国家研究基金会;

关键词：

Agent-based model; attraction; clustering; kinetic model; opinion formations; repulsion; CUCKER-SMALE FLOCKING; OPINION DYNAMICS; COLLECTIVE BEHAVIOR; MODEL; MATHEMATICS; PARTICLE; CULTURE;

D O I：

10.1142/S0218202512500133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss a first-order Cucker-Smale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

引用

页数：42

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