Fluctuation-induced collective motion: A single-particle density analysis

TL;DR

This paper analyzes how fluctuations and localized perturbations in a system of noisy self-propelled particles influence the emergence of collective motion, highlighting the roles of perturbation profile and particle speed.

Contribution

It introduces a single-particle density approach to identify conditions for collective motion, emphasizing the impact of perturbation shape and particle velocity.

Findings

Localized large angular perturbations can trigger collective motion.

Higher particle speeds promote the onset of collective behavior.

Threshold density for collective motion depends on perturbation profiles.

Abstract

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold may depend also on the profiles of the perturbation in the particle directions. Specifically, we perform mean-field, linear stability, perturbative and numerical analyses on an approximated form of the Fokker-Planck equation describing the system. We find that if an angular perturbation to an initially homogeneous system is large in magnitude and highly localized in space, it will be amplified and thus serves as an indication of the onset of collective motion. Our results also demonstrate that high particle speed promotes collective motion.