  The nonequilibrium stationary state of an exclusive genetic switch is
considered. The model comprises two competing species and a single binding site
which, when bound to by a protein of one species, causes the other species to
be repressed. The model may be thought of as a minimal model of the power
struggle between two competing parties. Exact solutions are given for the
limits of vanishing binding/unbinding rates and infinite binding/unbinding
rates. A mean field theory is introduced which is exact in the limit of
vanishing binding/unbinding rates. The mean field theory and numerical
simulations reveal that generically bistability occurs and the system is in a
symmetry broken state. An exact perturbative solution which in principle allows
the nonequilibrium stationary state to be computed is also developed and
computed to first and second order.
