  We derive methods for estimating the topology of the stationary probability
current $\vec{j}_s$ of the two-species Fokker-Planck equation (FPE) without the
need to solve the FPE. These methods are chosen such that they become exact in
certain limits, such as infinite system size or vanishing coupling between
species in the diffusion matrix. The methods make predictions about the fixed
points of $\vec{j}_s$ and their relation to extrema of the stationary
probability distribution and to fixed points of the convective field, which is
related to the deterministic drift of the system. Furthermore, they predict the
rotation sense of $\vec{j}_s$ around extrema of the stationary probability
distribution. Even though these methods cannot be proven to be valid away from
extrema, the boundary lines between regions with different rotation sense are
obtained with surprising accuracy. We illustrate and test these method using
simple reaction systems with only one coupling term between the two species as
well as a few generic reaction networks taken from literature. We use it also
to investigate the shape of non-physical probability currents occurring in
reaction systems with detailed balance due to the approximations involved in
deriving the Fokker-Planck equation.
