| 带局部交流函数及自由意志的单领导Cucker-Smale模型的渐近集群分析 |
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| 引用本文： | 赵子玉,刘易成.带局部交流函数及自由意志的单领导Cucker-Smale模型的渐近集群分析[J].国防科技大学学报,2022,44(3):10-15. |
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| 作者姓名： | 赵子玉 刘易成 |
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| 作者单位： | 国防科技大学文理学院,湖南长沙 410073 |
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| 基金项目： | 国家自然科学基金资助项目(11671011) |
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| 摘 要： | 为研究集群的形成与否和半径大小之间的关系,主要考虑了具有单个领导的一般等级结构及其领导者速度不变的Cucker-Smale模型。探讨了自由意志对集群产生的影响,通过证明可以给出半径有下界的充分条件(下界和速度差、粒子数、通信强度等有关)。当半径大于下界时,会产生集群。通过MATLAB数值仿真验证了相关结论。
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| 关 键 词： | Cucker-Smale模型 等级结构 自由意志 局部交流函数 粒子集群 |
| 收稿时间： | 2021/6/1 0:00:00 |
| 修稿时间： | 2022/4/28 0:00:00 |
Asymptotic cluster analysis of single-leader Cucker-Smale model with local interchange function and free will |
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| ZHAO Ziyu,LIU Yicheng.Asymptotic cluster analysis of single-leader Cucker-Smale model with local interchange function and free will[J].Journal of National University of Defense Technology,2022,44(3):10-15. |
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| Authors: | ZHAO Ziyu LIU Yicheng |
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| Institution: | College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China |
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| Abstract: | In order to study the relationship between cluster formation and radius, the Cucker-Smale model with a hierarchical structure of a single leader and the leader speed invariable was considered. The influence of free will on cluster was discussed. The sufficient conditions that the radius has a lower bound (the lower bound was related to the velocity difference, particle number, communication intensity, etc.) were obtained by proving. When the radius was greater than the lower bound, the cluster would be generated. The related conclusion was verified by MATLAB numerical simulation. |
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| Keywords: | the model of Cucker-Smale hierarchical organization free will local communication function clustering of particles |
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