Emergence of bi-cluster flocking for the Cucker-Smale model

doi:10.1142/S0218202516500287

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	Emergence of bi-cluster flocking for the Cucker-Smale model
	Cho, Junghee 1; Ha, Seung-Yeal 2; Huang, Feimin3,4 ; Jin, Chunyin 3,4; Ko, Dongnam 1
	2016-06-15
发表期刊	MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
ISSN	0218-2025
卷号	26 期号:6 页码:1191-1218
摘要	We present the mathematical analysis of bi-cluster flocking phenomenon for the short-ranged Cucker-Smale model with some well-prepared initial data. For this, we derive a system of differential inequalities for the functionals measuring the local spatial and velocity fluctuations and differences of local velocity averages, and then estimate the upper bound of spatial fluctuations and the lower bound of the difference between local velocity averages. We explicitly present an admissible class of initial configurations leading to the asymptotic emergence of bi-cluster flocking phenomenon. Unlike global flocking (a mono-cluster flocking configuration in velocity), where the convergence rate is always exponential, the asymptotic convergence to bi-cluster flocking configurations is affected by the far-field decay rate of communication weights so that it can be algebraic.
关键词	Cucker-Smale model local flocking slow relaxation bi-cluster flocking
DOI	10.1142/S0218202516500287
语种	英语
资助项目	Collaborative Research Project under the NRF-NSFC Cooperative Program
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000376383600005
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22783
专题	应用数学研究所
通讯作者	Ha, Seung-Yeal
作者单位	1.Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea 2.Seoul Natl Univ, Inst Math, Dept Math Sci & Res, Seoul 151747, South Korea 3.Acad Sinica, AMSS, Inst Appl Math, Beijing 100190, Peoples R China 4.Beijing Ctr Math & Informat Sci, Beijing 100048, Peoples R China
推荐引用方式 GB/T 7714	Cho, Junghee,Ha, Seung-Yeal,Huang, Feimin,et al. Emergence of bi-cluster flocking for the Cucker-Smale model[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2016,26(6):1191-1218.
APA	Cho, Junghee,Ha, Seung-Yeal,Huang, Feimin,Jin, Chunyin,&Ko, Dongnam.(2016).Emergence of bi-cluster flocking for the Cucker-Smale model.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,26(6),1191-1218.
MLA	Cho, Junghee,et al."Emergence of bi-cluster flocking for the Cucker-Smale model".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 26.6(2016):1191-1218.