JournalsaihpcVol. 38, No. 4pp. 1031–1053

A game of alignment: Collective behavior of multi-species

  • Siming He

    Department of Mathematics, Duke University, Durham, NC, United States of America
  • Eitan Tadmor

    Department of Mathematics, Institute for Physical Sciences & Technology, University of Maryland, College Park, MD, United States of America
A game of alignment: Collective behavior of multi-species cover
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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, ϕαβ\phi _{\alpha \beta }, 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\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.

Cite this article

Siming He, Eitan Tadmor, A game of alignment: Collective behavior of multi-species. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1031–1053

DOI 10.1016/J.ANIHPC.2020.10.003