2019/08/29 by He, Siming, Tadmor, Eitan
#35Q35 #76N10 #92D25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1908.11019
We study the (hydro-)dynamics of multi-species driven by alignment. What distinguishes the different species is the protocol of their interaction with the rest of the crowd: the collective motion is described by different communication kernels, ϕαβ, between the crowds in species α and β. We show that flocking of the overall crowd emerges provided the communication array between species forms a connected graph. In particular, the crowd within each species need not interact with its own kind, i.e., ϕαα=0; different species which are engaged in such `game' of alignment require a connecting path for propagation of information which will lead to the flocking of overall crowd. The same methodology applies to multi-species aggregation dynamics governed by first-order alignment: connectivity implies concentration around an emerging consensus.