Inthispaper,aperiodicHollingⅡpredator-preymodelwithimpulsiveeffectisinvestigated.ByapplyingtheFloquettheoryoflinearperiodicimpulsiveequation,somesufficientconditionsareobtainedforthelinearstabilityandinstabilityoftrivialandsemi-trivialperiodicsolutions.Moreover,weusestandardbifurcationtheorytoshowtheexistenceofcoexistencestateswhicharisenearthesemi-trivialperiodicsolution.Asanapplication,wealsoexaminesomespecialcaseofthesystemtoconfirmourmainresults.
