階級領導網路的離散型Cucker-Smale模型之雙群聚現象

Bi-cluster Flocking for Discrete-time Cucker-Smale Model with Hierarchical Leadership Networks

范氏和兒(Pham, Thi Hoa Nhi)

指導教授 ： 莊重

國立交通大學/理學院/應用數學系暨研究所/碩士(2020年)

摘要

在本文中，我們希望研究分層領導網絡下離散時間的雙群聚現象。 為了研究該模型，我們建立了適當的參數和初始條件，並使用給定的假設來確認每一組的群聚行為並且這兩組之間沒有群聚行為。 此外，我們還提供了一些模擬來說明我們的主要結果。
關鍵詞: 庫克-史邁爾模型, 雙群聚, 離散時間

關鍵字

庫克-史邁爾模型 ； 雙群聚 ； 離散時間

並列摘要

In this thesis, we wish to investigate the behavior of discrete-time bi-cluster flocking under the hierarchical leadership network. To investigate this model, we establish appropriate parameters and initial conditions, and use the given hypotheses to ensure that the flocking behavior within each one of two groups and no flocking between these two groups. Moreover, we also provide some simulations to illustrate our main results.
Keywords: Cucker-Smale model, bi-cluster flocking, discrete-time

並列關鍵字

Cucker-Smale model ； bi-cluster flocking ； discrete-time

參考文獻

[1] CHO, J. HA, S.-Y. HUANG, F. JIN, C. and KO, D., 2016. Emergence of bi-cluster flocking for the Cucker–Smale model. Mathematical Models and Methods in Applied Sciences, 26(06), pp.1191-1218.

[2] C. -H. LI AND S. -Y. YANG, A new discrete Cucker-Smale flocking model under hierarchical leadership, Discrete Contin. Dyn. Syst. Ser. B, 21(2016), pp.2587-2599.

[3] C. PIGNOTTI & I. R. VALLEJO, Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership. Journal of Mathematical Analysis and Applications, 464(2) (2018), 1313-1332.

[4] C.-W. WU, Synchronization in Complex Networks of Nonlinear Dynamical Systems, Singapore: World Scientific, (2007), pp. 88-89.

[5] D. FANG, S.-Y. HA, AND S. JIN, Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions (2018), arXiv preprint arXiv:1808.03980