Long time and large crowd dynamics of discrete Cucker-Smale alignment models
Abstract
We provide a bird's eye view on developments in analyzing the long time, large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of (fully-)discrete models, paying particular attention to general alignment protocols in which agents, with possibly time-dependent masses, are driven by a large class of heavy-tailed communication kernels. The presence of time-dependent masses allows, in particular, non-symmetric communication. While revisiting known results in the literature, we also shed new light of various aspects on the long time flocking/swarming behavior, driven by the decay of energy fluctuations and heavy-tailed connectivity. We also discuss the large crowd dynamics in terms of the hydrodynamic description of Euler alignment models.
Keywords
Cite
@article{arxiv.2201.02281,
title = {Long time and large crowd dynamics of discrete Cucker-Smale alignment models},
author = {Eitan Tadmor},
journal= {arXiv preprint arXiv:2201.02281},
year = {2023}
}