A previously unreported regime of type III intermittency is observed in a vertically vibrated milliliter-sized liquid drop submerged in a more viscous and less dense immiscible fluid layer supported by a hydrophobic solid plate. As the vibration amplitude is gradually increased, subharmonic Faraday waves are excited at the upper surface of the drop. We find a narrow window of vibration amplitudes slightly above the Faraday threshold, where the drop exhibits an irregular sequence of large amplitude bursting events alternating with intervals of low amplitude activity. The triggering physical mechanism is linked to the competition between surface Faraday waves and the shape deformation mode of the drop.
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