  We predict the spontaneous modulated emission from a pair of
exciton-polariton condensates due to coherent (Josephson) and dissipative
coupling. We show that strong polariton-polariton inter- action generates
complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a
result, the exciton-polariton condensates exhibit self-induced oscillations and
emit an equidistant frequency comb light spectrum. A plethora of possible
emission spectra with asymmetric peak dis- tributions appears due to
spontaneously broken time-reversal symmetry. The lasing dynamics is affected by
the shot noise arising from the influx of polaritons. That results in a complex
inhomo- geneous line broadening.
