Singular perturbation analysis of a reduced model for collective motion: A renormalization group approach

TL;DR

This paper uses a renormalization group approach to analyze how initial perturbations affect the critical density for collective motion in a model of noisy self-propelled particles, providing analytical insights into the system's behavior.

Contribution

It introduces a renormalization-group improved perturbative method to determine the influence of initial perturbations on the critical density in a collective motion model.

Findings

Critical density depends on initial angular perturbation strength.

Analytical expression for critical density modification derived.

First-order perturbation analysis applied to the model equations.

Abstract

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determine how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations, and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.