  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.
