Swarming transitions in hierarchical societies

TL;DR

This paper investigates how social hierarchy influences the nature of swarming transitions, revealing that increasing hierarchy strength alters the transition from weak to strong first-order and eventually suppresses it in despotic societies.

Contribution

It introduces a hierarchical swarm model extending the Vicsek model, demonstrating how hierarchy strength affects the order-disorder transition in collective movement.

Findings

Swarming transition changes from weak to strong first-order with increasing hierarchy.

In extremely despotic societies, the transition disappears, indicating no order-disorder phase change.

Hierarchy significantly influences the spatial structure and correlation within the swarm.

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.