Solitary states in the mean-field limit

TL;DR

This paper investigates solitary states in active matter systems with second order dynamics, analyzing their emergence via bifurcations, their stochastic versions, and phase transitions in the mean-field limit using analytical and numerical methods.

Contribution

It introduces a continuum Kuramoto model with inertia and noise, linking solitary states to phase transitions and providing a comprehensive analysis of active matter dynamics.

Findings

Solitary states emerge via homoclinic bifurcation.

Stochastic solitary states are characterized with noise.

Second order phase transition between polar order and disorder.

Abstract

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.