Density regulation in strictly metric-free swarms

TL;DR

This paper introduces a new model for metric-free bird flocking that maintains stable density through a motional bias on edge individuals, revealing a power-law density scaling and an order-disorder transition.

Contribution

It proposes a simple, two-parameter metric-free model with a novel edge-based motional bias to regulate density in swarms.

Findings

Density scales as a power-law with the number of individuals.

The model exhibits an order-to-disorder phase transition.

Stable density is achieved without artificial constraints.

Abstract

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition.