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1、AcceptedManuscriptHopfbifurcationandcenterstabilityforapredator-preybiologicaleconomicmodelwithpreyharvestingWeiLiu,ChaojinFu,BoshanChenPII:S1007-5704(12)00082-2DOI:10.1016/j.cnsns.2012.02.025Reference:CNSNS2381Toappearin:CommunicationsinNonlinearSciencean
2、dNumer‐icalSimulationReceivedDate:5December2010RevisedDate:13November2011AcceptedDate:17February2012Pleasecitethisarticleas:Liu,W.,Fu,C.,Chen,B.,Hopfbifurcationandcenterstabilityforapredator-preybiologicaleconomicmodelwithpreyharvesting,CommunicationsinNon
3、linearScienceandNumericalSimulation(2012),doi:10.1016/j.cnsns.2012.02.025ThisisaPDFfileofanuneditedmanuscriptthathasbeenacceptedforpublication.Asaservicetoourcustomersweareprovidingthisearlyversionofthemanuscript.Themanuscriptwillundergocopyediting,typeset
4、ting,andreviewoftheresultingproofbeforeitispublishedinitsfinalform.Pleasenotethatduringtheproductionprocesserrorsmaybediscoveredwhichcouldaffectthecontent,andalllegaldisclaimersthatapplytothejournalpertain.Hopfbifurcationandcenterstabilityforapredator-prey
5、biologicaleconomicmodelwithpreyharvestingWeiLiu1,ChaojinFu2,BoshanChen∗21SchoolofMathematicsandComputerScience,XinyuUniversity,Xinyu,Jiangxi,China2CollegeofMathematicsandStatistics,HubeiNormalUniversity,Huangshi,Hubei,ChinaAbstractInthispaper,weinvestigate
6、Hopfbifurcationandcenterstabilityofapredator-preybiologicaleco-nomicmodel.Byemployingthelocalparameterizationmethod,Hopfbifurcationtheoryandtheformalseriesmethod,weobtainsometestableresultsontheseissues.Theeconomicprofitischosenasapositivebifurcationparamet
7、erhere.ItshowsthataphenomenonofHopfbifurcationoccursastheeconomicprofitincreasesbeyondacertainthreshold.Besides,wealsofindthatthecenterofthebiologicaleconomicmodelisalwaysunstable.Finally,somenumericalsimulationsaregiventoillustratetheeffectivenessofourresult
8、s.Keywords:Hopfbifurcation;Harvesting;Stability;Differential-algebraicsystem.1IntroductionInrecentyears,thedynamicsofprey-predatormodelswithharvestinghavebeenwidelystudiedbymanyauthors[4-13]andthereferencesthe
