TY - JOUR T1 - Dynamics Analysis for a Hierarchical System with Nonlinear Cut-off Interaction and Free Will AU - Zhao , Ziyu AU - Liu , Yicheng AU - Wang , Xiao JO - Analysis in Theory and Applications VL - 1 SP - 38 EP - 56 PY - 2024 DA - 2024/04 SN - 40 DO - http://doi.org/10.4208/ata.OA-2021-0004 UR - https://global-sci.org/intro/article_detail/ata/23019.html KW - Motsch-Tadmor model, hierarchical structure, free will, flocking behavior. AB -

Noting that the particles communicate with each other within a finite distance, 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 coefficient to achieve the flocking behavior. Besides we will use energy function to achieve some sufficient conditions to achieve a flock. 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.