EMERGENCE OF STOCHASTIC FLOCKING FOR THE DISCRETE CUCKER-SMALE MODEL WITH RANDOMLY SWITCHING TOPOLOGIES

被引：0

作者：

Dong, Jiu-Gang ^{[1
]}

Ha, Seung-Yeal ^{[2
,3
,4
]}

Jung, Jinwook ^{[5
]}

Kim, Doheon ^{[4
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[3] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[4] Korea Inst Adv Study, Sch Math, Hoegiro 85, Seoul 02455, South Korea

[5] Seoul Natl Univ, Res Inst Basic Sci, Seoul 08826, South Korea

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2021年 / 19卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Cucker-Smale model; randomly switching topology; directed graphs; flocking; ASYMPTOTIC FLOCKING; DYNAMICS; BEHAVIOR; SYNCHRONIZATION; LEADERSHIP; NETWORKS; PARTICLE; SUBJECT;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study emergent dynamics of the discrete Cucker-Smale (in short, DCS) model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient framework is formulated in terms of an admissible set of network topologies realized by digraphs and probability density function for random switching times. As examples for the law of switching times, we use the Poisson process and the geometric process and show that these two processes satisfy the required conditions in a given framework so that we have a stochastic flocking with probability one. As a corollary of our flocking analysis, we improve the earlier result [J.-G. Dong, S.-Y. Ha, J. Jung, and D. Kim, SIAM J. Control Optim., 58(4):2332-2353, 2019] on the continuous CS model.

引用

页码：205 / 228

页数：24

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