简介：Inthispaper,weproposeaLotka-Volterraprey-predatorsystemwithdiscretedelaysandfeedbackcontrol.Firstly,weshowthatsolutionofthesystemisbounded.Secondly,weobtainsufficientconditionfortheglobalstabilityoftheuniquepositiveequilibriumtothesystem.

简介：Inthispaper,wepresentastabilityanalysisofaLotka-VolterracommensalsymbiosismodelsubjecttoAlleeeffectontheunaffectedpopulationwhichoccursatlowpopulationdensity.ByanalyzingtheJacobianmatrixaboutthepositiveequilibrium,weshowthatthepositiveequilibriumislocallyasymptoticallystable.Byapplyingthedifferentialinequalitytheory,weshowthatthesystemispermanent,consequently,theboundaryequilibriaofthesystemisunstable.Finally,byusingtheDulaccriterion,weshowthatthepositiveequilibriumisgloballystable.AlthoughAlleeeffecthasnoinfluenceonthefinaldensitiesofthepredatorandpreyspecies,numericsimulationsshowthatthesystemsubjecttoanAlleeeffecttakesmuchlongertimetoreachitsstablesteady-statesolution,inthissensethatAlleeeffecthasunstableeffectonthesystem,however,suchaneffectiscontrollable.Suchanfindingisgreatlydifferenttothatofthepredator-preymodel.