A game of alignment:collective behavior of multi-species

Abstract: 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, $\phi_{\alpha\beta}$, between the crowds in species $\alpha$ and $\beta$. 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., $\phi_{\alpha\alpha}=0$; 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.