@Article{ATA-40-38, author = {Zhao , ZiyuLiu , Yicheng and Wang , Xiao}, 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 = {
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.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0004}, url = {http://global-sci.org/intro/article_detail/ata/23019.html} }