@Article{ATA-40-1,
author = {Ziyu, Zhao and Yicheng, Liu and Xiao, Wang},
title = {Dynamics Analysis for a Hierarchical System with Nonlinear Cut-off Interaction and Free Will},
journal = {Analysis in Theory and Applications},
year = {2024},
volume = {40},
number = {1},
pages = {38--56},
abstract = {<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>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2021-0004},
url = {https://global-sci.com/article/90891/dynamics-analysis-for-a-hierarchical-system-with-nonlinear-cut-off-interaction-and-free-will}
}