KMS Of Academy of mathematics and systems sciences, CAS
| Emergence of bi-cluster flocking for the Cucker-Smale model | |
Cho, Junghee1; Ha, Seung-Yeal2; Huang, Feimin3,4 ; Jin, Chunyin3,4; Ko, Dongnam1
| |
| 2016-06-15 | |
| Source Publication | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
 |
| ISSN | 0218-2025 |
| Volume | 26Issue:6Pages:1191-1218 |
| Abstract | 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. |
| Keyword | Cucker-Smale model local flocking slow relaxation bi-cluster flocking |
| DOI | 10.1142/S0218202516500287 |
| Language | 英语 |
| Funding Project | Collaborative Research Project under the NRF-NSFC Cooperative Program |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000376383600005 |
| Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/22783 |
| Collection | 应用数学研究所 |
| Corresponding Author | Ha, Seung-Yeal |
| Affiliation | 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 |
| Recommended Citation 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment