| 周晨昕,刘宏亮,欧阳自根.受邻居影响的热力学Cucker-Smale模型的集群[J].南华大学学报(自然科学版),2023,(2):82~90.[ZHOU Chenxin,LIU Hongliang,OUYANG Zigen.Flocking of Thermodynamic Cucker-Smale Models Affected by Neighbors[J].Journal of University of South China(Science and Technology),2023,(2):82~90.] |
| 受邻居影响的热力学Cucker-Smale模型的集群 |
| Flocking of Thermodynamic Cucker-Smale Models Affected by Neighbors |
| 投稿时间：2022-09-26 |
| DOI：10.19431/j.cnki.1673-0062.2023.02.012 |
| 中文关键词: 热力学Cucker-Smale模型 图论 渐近集群 |
| 英文关键词:thermodynamic Cucker-Smale model graph theory symptotic flocking |
| 基金项目:湖南省自然科学基金项目(2020JJ6003;2021JJ30567);湖南省教育厅重点项目(20A425) |
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| 中文摘要: |
| 针对受最近邻居影响下的连续热力学Cucker-Smale模型的集群问题,本文基于图论和状态转移矩阵相关理论进行分析,并且结合Peano-Baker数列,证明了系统中粒子个数q≥N－12时,系统发生无条件集群,并给出数值模拟例子验证了结论的正确性。 |
| 英文摘要: |
| For the flocking problem of continuous thermodynamic Cucker-Smale model under the influence of the nearest neighbor model, based on graph theory and state transition matrix theory, and combined with the Peano-Baker series, it is proved that when the number of particles q≥N－12 in the system, unconditional clustering occurs. Finally, the correctness of the conclusion is verified by numerical simulation. |
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