Mean field theory of chaotic insect swarms

Abstract

The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale free transition between single and multicluster chaotic phases. Finite size scaling indicates that this unusual phase transition occurs at zero confinement [Physical Review E 107, 014209 (2023)]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent $z=1$ and a new critical exponent $\phi =0.5$ for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor), and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.

15 pages, 10 figures, including supplementary material, revtex

References in corpus (6)

• Novel type of phase transition in a system of self-driven particles
• Finite-size scaling as a way to probe near-criticality in natural swarms
• Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
• Natural Swarms in $3.99$ Dimensions
• Scale free chaos in the confined Vicsek flocking model
• Equilibrium to off-equilibrium crossover in homogeneous active matter

Cited by in corpus (3)

• Scale-free chaos in the 2D harmonically confined Vicsek model
• Power laws of natural swarms are fingerprints of an extended critical region
• The Inertial Spin Model of flocking with position-dependent forces