Geodesic
A game of alignment: Collective behavior of multi-species
He, Siming1 ; Tadmor, Eitan2
1 a Department of Mathematics, Duke University, Durham, NC, United States of America
2 b Department of Mathematics, Institute for Physical Sciences & Technology, University of Maryland, College Park, MD, United States of America
Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1031-1053

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.10.003
Classification : 92D25, 35Q35, 76N10
Keywords: Collective behavior, Alignment, Aggregation, Multi-species, Connected graph, Weighted Poincaré inequality

He, Siming 1 ; Tadmor, Eitan 2

1 a Department of Mathematics, Duke University, Durham, NC, United States of America
2 b Department of Mathematics, Institute for Physical Sciences & Technology, University of Maryland, College Park, MD, United States of America 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :