Boundary information inflow enhances correlation in flocking

TL;DR

This paper demonstrates through simulations and theory that boundary information inflow can produce long-range correlations in flocking behavior, explaining the small decay exponent observed in starling flocks.

Contribution

It introduces a boundary-driven dynamical field model that explains long-range correlations in collective animal behavior, bridging a gap in existing theories.

Findings

Boundary inflow induces long-range correlations in spin models.

The model reproduces the small decay exponent observed in starling flocks.

Both environmental and internal factors can generate boundary information inflow.

Abstract

The most conspicuous trait of collective animal behaviour is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial correlations. Experimental data on starling flocks in 3d show that the exponent ruling the decay of the velocity correlation function, C(r) ~ 1/r^\gamma, is extremely small, \gamma << 1. This result can neither be explained by equilibrium field theory, nor by off-equilibrium theories and simulations of active systems. Here, by means of numerical simulations and theoretical calculations, we show that a dynamical field applied to the boundary of a set of Heisemberg spins on a 3d lattice, gives rise to a vanishing exponent \gamma, as in starling flocks. The effect of the dynamical field is to create an information inflow from border to bulk that triggers long range spin wave modes, thus giving rise to an anomalously long-ranged correlation. The biological origin of this phenomenon can be either exogenous - information produced by environmental perturbations is transferred from boundary to bulk of the flock - or endogenous - the flock keeps itself in a constant state of dynamical excitation that is beneficial to correlation and collective response.