Swarming transitions in hierarchical societies

Tingting Xue,Xu Li,Peter Grassberger,Li Chen

doi:10.1103/physrevresearch.2.042017

Tingting Xue, Xu Li + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.2.042017

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Abstract

Social hierarchy is central to decision-making in the coordinated movement of many swarming species. Here we propose a hierarchical swarm model in the spirit of the Vicsek model of self-propelled particles. We show that, as the hierarchy becomes important, the swarming transition changes from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and finally the discontinuity reduces till vanish, where the order-disorder transition appears to be absent in the extremely despotic societies. Associated to this we observe that the spatial structure of the swarm, as measured by the correlation between the density and velocity fields, is strongly mediated by the hierarchy. A two-group model and vectorial noise are also studied for verification. Our results point out the particular relevance of the hierarchical structures to swarming transitions when doing specific case studies.

Highlights

Collective motion is one of most spectacular and fascinating emergent behaviors in nature, as exhibited in insects, bird flocks, fish shoals, and herds of ungulates, among others [1]
As the hierarchy becomes important, the swarming transition changes from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and the discontinuity reduces until vanish, where the order-disorder transition appears to be absent in the extremely despotic societies
The second-order phase transition (PT) claimed in the original work was later challenged by Cháte and co-workers [9,10], by showing that the observed continuous nature is due to finite-size effects, and a first-order transition should be expected in the thermodynamical limit if only with local interactions—in line with some theoretical studies [11,12,13]

Summary

Introduction

Collective motion is one of most spectacular and fascinating emergent behaviors in nature, as exhibited in insects, bird flocks, fish shoals, and herds of ungulates, among others [1]. A major concern here is the nature of swarming transitions between the ordered and disordered states of movement. We fill this gap by introducing a hierarchical swarm model, called the hierarchical Viscek model (HVM), and investigate the impact of the hierarchy on the nature of order-disorder transitions. J: di j

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Results and analysis

Conclusions