Year: 2024
Author: Ziyu Zhao, Yicheng Liu, Xiao Wang
Analysis in Theory and Applications, Vol. 40 (2024), Iss. 1 : pp. 38–56
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2021-0004
Analysis in Theory and Applications, Vol. 40 (2024), Iss. 1 : pp. 38–56
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Motsch-Tadmor model hierarchical structure free will flocking behavior.