{"title":"Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions","authors":"Chun Yin Jin, Shuang Zhi Li","doi":"10.1007/s10114-024-2127-0","DOIUrl":null,"url":null,"abstract":"<div><p>How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory. Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance (cf. Motsch and Tadmor in J. Stat. Phys. 2011). In this paper, we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions. Using properties of a connected stochastic matrix, together with an elaborate analysis on perturbations of a linearized system, we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking. Moreover, it is shown that the system achieves flocking at an exponential rate.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-2127-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory. Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance (cf. Motsch and Tadmor in J. Stat. Phys. 2011). In this paper, we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions. Using properties of a connected stochastic matrix, together with an elaborate analysis on perturbations of a linearized system, we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking. Moreover, it is shown that the system achieves flocking at an exponential rate.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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