  We consider a general class of autocatalytic reactions, that has been shown
to display stochastically switching behaviour (Discreteness Induced
Transitions) in some parameter regimes. This behaviour was shown to occur when
either the overall species count is low, or when the rate of inflow and outflow
of species is relatively much smaller than the rate of autocatalytic reactions.
The long-term behaviour of this class was analyzed in \cite{KBW20} with an
analytic formula for the stationary distribution in the symmetric case. We
focus on the case of asymmetric autocatalytic reactions and provide a formula
for an approximate stationary distribution of the model. We show this
distribution has different properties corresponding to the distinct behaviour
of the process in the three parameter regimes. In the Discreteness Induced
Transitions regime, the formula provides the fraction of time spent at each of
the stable points.
