We study a planar stochastic differential equation with additive noise for which the rotational speed is of the form ρ(R) where R is the radial part.

We investigate how phenomena like strong or weak synchronization, existence of a pullback or a point attractor and strong completeness of the associated random dynamical system depend on the function ρ. This is joint work (in progress) with Maximilian Engel and Dennis Chemnitz (FU Berlin).