  We propose a method to obtain phase portraits for stochastic systems.
Starting from the Fokker-Planck equation, we separate the dynamics into a
convective and a diffusive part. We show that stable and unstable fixed points
of the convective field correspond to maxima and minima of the stationary
probability distribution if the probability current vanishes at these points.
Stochastic phase portraits, which are vector plots of the convective field,
therefore indicate the extrema of the stationary distribution and can be used
to identify stochastic bifurcations that change the number and stability of
these extrema. We show that limit cycles in stochastic phase portraits can
indicate ridges of the probability distribution, and we identify a novel type
of stochastic bifurcations, where the probability maximum moves to the edge of
the system through a gap between the two nullclines of the convective field.
