  Recent study demonstrated that steady states of a polariton system may show a
first-order dissipative phase transition with an exceptional point that appears
as an endpoint of the phase boundary [R. Hanai et al., Phys. Rev. Lett. 122,
185301 (2019)]. Here, we show that this phase transition is strictly related to
the stability of solutions. In general, the exceptional point does not
correspond to the endpoint of a phase transition, but rather it is the point
where stable and unstable solutions coalesce. Moreover, we show that the
transition may occur also in the weak coupling regime, which was excluded
previously. In a certain range of parameters, we demonstrate permanent
Rabi-like oscillations between light and matter fields. Our results contribute
to the understanding of nonequilibrium light-matter systems, but can be
generalized to any two-component oscillatory systems with gain and loss.
