Long time and large crowd dynamics of discrete Cucker-Smale alignment models

2022/01/07 by Tadmor, Eitan
#35Q35 #70F40 #92D25 #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2201.02281

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.

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