  We investigate the relation between the stationary probability distribution
of chemical reaction systems and the convective field derived from the chemical
Fokker-Planck equation (CFPE) by comparing predictions of the convective field
to the results of stochastic simulations based on Gillespie's algorithm. The
convective field takes into account the drift term of the CFPE and the reaction
bias introduced by the diffusion term. For one-dimensional systems, fixed
points and bifurcations of the convective field correspond to extrema and
phenomenological bifurcations of the stationary probability distribution
whenever the CFPE is a good approximation to the stochastic dynamics. This
provides an efficient way to calculate the effect of system size on the number
and location of probability maxima and their phenomenological bifurcations in
parameter space. For two-dimensional systems, we study models that have
saddle-node and Hopf bifurcations in the macroscopic limit. Here, the existence
of two stable fixed points of the convective field correlates either with two
peaks of the stationary probability distribution, or with a peak and a
shoulder. In contrast, a Hopf bifurcation that occurs in the convective field
for decreasing system size is not accompanied by the onset of a crater-shaped
probability distribution; decreasing system size rather destroys craters and
replaces them by local maxima.

Statistical Mechanics;Molecular Networks