数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 632-649.doi: 10.1007/s10473-024-0214-z

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FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

Chunyin JIN*, Shuangzhi LI   

  1. College of Science, China Agricultural University, Beijing 100083, China
  • 收稿日期:2023-02-28 修回日期:2023-06-28 出版日期:2024-04-25 发布日期:2024-04-16
  • 通讯作者: *Chunyin JIN, E-mail: jinchunyin@163.com
  • 作者简介:Shuangzhi LI, E-mail: lsz1006237128@163.com
  • 基金资助:
    Jin's work was supported by the NSFC (12001530).

FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

Chunyin JIN*, Shuangzhi LI   

  1. College of Science, China Agricultural University, Beijing 100083, China
  • Received:2023-02-28 Revised:2023-06-28 Online:2024-04-25 Published:2024-04-16
  • Contact: *Chunyin JIN, E-mail: jinchunyin@163.com
  • About author:Shuangzhi LI, E-mail: lsz1006237128@163.com
  • Supported by:
    Jin's work was supported by the NSFC (12001530).

摘要: In this paper, we study the flocking behavior of a thermodynamic Cucker-Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

关键词: flocking, local interaction, thermodynamical Cucker-Smale model, stochastic matrix, neighbor graph

Abstract: In this paper, we study the flocking behavior of a thermodynamic Cucker-Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

Key words: flocking, local interaction, thermodynamical Cucker-Smale model, stochastic matrix, neighbor graph

中图分类号: 

  • 34A36