摘要
Inthispaper,wepresentastabilityanalysisofaLotka-VolterracommensalsymbiosismodelsubjecttoAlleeeffectontheunaffectedpopulationwhichoccursatlowpopulationdensity.ByanalyzingtheJacobianmatrixaboutthepositiveequilibrium,weshowthatthepositiveequilibriumislocallyasymptoticallystable.Byapplyingthedifferentialinequalitytheory,weshowthatthesystemispermanent,consequently,theboundaryequilibriaofthesystemisunstable.Finally,byusingtheDulaccriterion,weshowthatthepositiveequilibriumisgloballystable.AlthoughAlleeeffecthasnoinfluenceonthefinaldensitiesofthepredatorandpreyspecies,numericsimulationsshowthatthesystemsubjecttoanAlleeeffecttakesmuchlongertimetoreachitsstablesteady-statesolution,inthissensethatAlleeeffecthasunstableeffectonthesystem,however,suchaneffectiscontrollable.Suchanfindingisgreatlydifferenttothatofthepredator-preymodel.
出版日期
2018年04月14日（中国Betway体育网页登陆平台首次上网日期，不代表论文的发表时间）
