Before revision:  For one-dimensional systems, fixed points and bifurcations of the convective field correspond to extrema and phenomenological bifurcations of the stationary probability distribution as long as the CFPE is a good approximation to the stochastic dynamics.
After revision:  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.