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Can bursts in dynamical systems be synchronized by a weak, common, noise background? We observe large, uncorrelated bursts of intensity fluctuations in two almost identical erbium-doped fiber ring lasers, initiated by common injection of a weak, constant intensity optical signal. Significant synchronization of the bursts is obtained for noise and sinusoidal modulation of the injected light intensity. Measurements of the burst statistics and synchronization are presented.