• Publisher-DOI

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.

Self-organization in large collectives of interacting particles is a fascinating phenomenon that is not completely understood. We study how spatially homogeneous particle ensembles behave subject to second-order rules of motion. Spatial homogeneity allows us to simplify the description of particle dynamics to that of their orientations only. This leads us to the Kuramoto model with inertia and allows us to regard particles as network oscillators, for which solitary states that naturally arise in systems of coupled pendula and power grids have recently been discovered. The goal of this study is to analyze the appearance of solitary states from the point of view of the active matter theory, particularly in the mean-field limit and under the influence of noise.