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 interaction
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 distributions 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 inhomogeneous line broadening.