We consider nonlinear dynamics of a system of interacting photons and
excitons driven by a resonantly exciting light field. Using the linear
stability analysis for nonlinear coupled equations of photon and exci
ton operators we investigated that, besides the usual unstable domain
which is a negative slope branch, there are other unstable ones in the
leftmost and rightmost sides of the lower and upper branches of the f
requency-density bistable curves. Numerical study shows that the syste
m has very rich information on the instability nature and a self-oscil
lation process leading to chaos can occur in these unstable domains.