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, , 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., ; 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.
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.10.003
Mots-clés : Collective behavior, Alignment, Aggregation, Multi-species, Connected graph, Weighted Poincaré inequality
@article{AIHPC_2021__38_4_1031_0,
author = {He, Siming and Tadmor, Eitan},
title = {A game of alignment: {Collective} behavior of multi-species},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1031--1053},
publisher = {Elsevier},
volume = {38},
number = {4},
year = {2021},
doi = {10.1016/j.anihpc.2020.10.003},
mrnumber = {4266234},
zbl = {1466.92146},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.anihpc.2020.10.003/}
}
TY - JOUR AU - He, Siming AU - Tadmor, Eitan TI - A game of alignment: Collective behavior of multi-species JO - Annales de l'I.H.P. Analyse non linéaire PY - 2021 SP - 1031 EP - 1053 VL - 38 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2020.10.003/ DO - 10.1016/j.anihpc.2020.10.003 LA - en ID - AIHPC_2021__38_4_1031_0 ER -
%0 Journal Article %A He, Siming %A Tadmor, Eitan %T A game of alignment: Collective behavior of multi-species %J Annales de l'I.H.P. Analyse non linéaire %D 2021 %P 1031-1053 %V 38 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2020.10.003/ %R 10.1016/j.anihpc.2020.10.003 %G en %F AIHPC_2021__38_4_1031_0
He, Siming; Tadmor, Eitan. A game of alignment: Collective behavior of multi-species. Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1031-1053. doi : 10.1016/j.anihpc.2020.10.003. http://www.numdam.org/articles/10.1016/j.anihpc.2020.10.003/
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