Scale free chaos in swarms

Abstract

Swarms are examples of collective behavior of insects, which are singular among manifestations of flocking. Swarms possess strong correlations but no global order and exhibit finite-size scaling with a dynamic critical exponent z ≈ 1. We have discovered a phase transition of the three-dimensional harmonically confined Vicsek model that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos that can be characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. Their critical exponents agree with those observed in natural midge swarms, unlike values obtained from the order-disorder transition of the standard Vicsek model which confines particles by artificial periodic boundary conditions.