Dynamics Analysis for a Hierarchical System with Nonlinear Cut-Off Interaction and FreeWill  

作　　者：Ziyu Zhao Yicheng Liu Xiao Wang 

机构地区：[1]College of Liberal Arts and Science,National University of Defense Technology,Changsha,Hunan 410073,China

出　　处：《Analysis in Theory and Applications》2024年第1期38-56,共19页分析理论与应用（英文刊）

基　　金：supported by the National Natural Science Foundation of China(No.11671011);Hunan Provincial Innovation Foundation for Postgraduate(CN)(No.CX20200011).

摘　　要：Noting that the particles communicate with each other within afinite dis-tance,in the paper,we investigate the hierarchical model with free will and cut-off function(linear or nonlinear).As our observation,the cut-off size r is a sensitive coef-ficient to achieve theflocking behavior.Besides we will use energy function to achieve some sufficient conditions to achieve aflock.The free-will represents the tendency of the particle itself to move.It will either facilitate or prevent cluster generation.Some numerical simulations will validate our conclusions.

关 键 词：Motsch-Tadmor model hierarchical structure free will flocking behavior 

分 类 号：O17[理学—数学]