Weinvestigatemodulationalinstability(MI)ofacoupledtwo-componentBose–Einsteincondensatesinarotatingringtrap.TheexcitationspectrumandtheMIconditionofthesystemarepresentedanalytically.WefindthatthecouplingbetweenthetwocomponentsstronglymodifiestheMIcondition,andtheMIconditionisphase-dependent.Furthermore,wediscusstheeffectofMIonbothdensityexcitationandspinexcitation.Iftheinter-andintra-componentinteractionstrengthsareallequal,theMIcausesdensityexcitationbutnotspinexcitation,andiftheinter-andintracomponentinteractionstrengthsaredifferent,theMIcausesbothdensityexcitationandspinexcitation.Ourresultsprovideapromisingapproachforcontrollingthestabilityandexcitationofarotatingtwo-componentBose–Einsteincondensatesbymodulatingitscouplingstrengthandinteractionstrength.
