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.
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