Non-emergence of mono-cluster flocking and multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint

IF 1.2 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Networks and Heterogeneous Media Pub Date : 2023-01-01 DOI:10.3934/nhm.2023066

Hyunjin Ahn

引用次数: 0

Abstract

This paper demonstrates several sufficient frameworks for the mono-cluster flocking, the non-emergence of mono-cluster flocking and the multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint (say TCSUS). First, in a different way than [2], we present the admissible data for the mono-cluster flocking of TCSUS to occur. Second, we prove that when the coupling strength is less than some positive value, mono-cluster flocking does not occur in the TCSUS system with an integrable communication weight. Third, motivated from the study on coupling strengths where the mono-cluster flocking does not occur, we investigate appropriate sufficient frameworks to derive the multi-cluster flocking of the TCSUS system.

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单位速度约束下热力学cucker - small模型的不出现单簇和多簇群集

本文给出了具有单位速度约束的热力学cucker - small模型(如TCSUS)的单簇群集、不出现单簇群集和多簇群集的几个充分的框架。首先，以与[2]不同的方式，我们提供了发生TCSUS单集群群集的可接受数据。其次，我们证明了当耦合强度小于某个正值时，具有可积通信权值的TCSUS系统不会发生单簇群集。第三，从对不存在单集群集群的耦合强度的研究出发，探讨了适当的、充分的框架来推导TCSUS系统的多集群集群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Networks and Heterogeneous Media 数学-数学跨学科应用

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： NHM offers a strong combination of three features: Interdisciplinary character, specific focus, and deep mathematical content. Also, the journal aims to create a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation. NHM publishes original contributions of high quality in networks, heterogeneous media and related fields. NHM is thus devoted to research work on complex media arising in mathematical, physical, engineering, socio-economical and bio-medical problems.