{"title":"Strong stochastic flocking with noise under long-range fat tail communication","authors":"Rundong Zhao, Yicheng Liu, Xiao Wang, Xuying Xiong","doi":"10.1007/s12190-024-02128-x","DOIUrl":null,"url":null,"abstract":"<p>Consider the reality that flocking behavior is affected by random noise. We study the Cucker–Smale-type systems with multiplicative noise where the communication weight satisfies the long-range fat tail condition. By comparing with the related deterministic system, we show that the noise intensity of the stochastic system mainly affects the convergence speed of the flocking. Specifically, we demonstrate that the system can achieve a stochastic finite-time flocking when the noise intensity is small, and almost surely asymptotic flocking when the noise intensity is large. Some numerical simulations are given to show our theoretical results. In addition, the method in this work can improve the results of previous studies.\n</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"30 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02128-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Consider the reality that flocking behavior is affected by random noise. We study the Cucker–Smale-type systems with multiplicative noise where the communication weight satisfies the long-range fat tail condition. By comparing with the related deterministic system, we show that the noise intensity of the stochastic system mainly affects the convergence speed of the flocking. Specifically, we demonstrate that the system can achieve a stochastic finite-time flocking when the noise intensity is small, and almost surely asymptotic flocking when the noise intensity is large. Some numerical simulations are given to show our theoretical results. In addition, the method in this work can improve the results of previous studies.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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