A game of alignment: Collective behavior of multi-species

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.10.003

Siming He , Eitan Tadmor

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引用次数: 13

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, $ϕ_{α β}$ , 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., $ϕ_{α α} = 0$ ; 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.

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结盟游戏:多物种的集体行为

我们研究了多物种在排列驱动下的(水)动力学。区分不同物种的是它们与群体其他成员相互作用的协议:集体运动是用物种α和β群体之间不同的通信核(ϕαβ)来描述的。我们表明，当物种之间的通信阵列形成连通图时，总体群体就会出现群集。特别是，每个物种内的群体不需要与自己的同类相互作用，即，ϕαα=0;参与这种“游戏”的不同物种需要一条信息传播的连接路径，这将导致整体群体的聚集。同样的方法也适用于由一阶对齐控制的多物种聚集动力学:连通性意味着围绕新兴共识的集中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.