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 - <p style="text-align: justify;">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.</p>