资源描述：
《A predator–prey model with disease in the》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、NonlinearAnalysis36(1999)747{766Apredator-preymodelwithdiseaseinthepreyJ.Chattopadhyaya,O.ArinobaEmbryologyResearchUnit,IndianStatisticalInstitute,203,B.T.Road,Calcutta700035,IndiabUPRESA5033,IPRA,UniversityofPau,64000Pau,FranceReceived20May1997;accepted23December1997Keyword
2、s:Soundprey;Infectedprey;Predator;Hopfbifurcation;Poincaremap1.IntroductionAftertheseminalmodelsofVitoVolterraandAlfredJamesLotkainthemid1920sforpredator-preyinteractions,mutualistandcompetitivemechanismshavebeenstudiedextensivelyintherecentyearsbyresearchers.Therearesomany
3、referencesinthiscontext,wehavejustcitedheresomebooks(e.g.see,[14,16{18,?]andtherefer-encestherein).Similarly,afterthepioneeringworkofKermack{McKendrickonSIRS(susceptible-infective-removal-susceptible)epidemiologicalmodelshavealsoreceivedmuchattentionfromscientists.Relevantre
4、ferencesinthiscontextarealsovastandweshallagainmentionheresomebooks(see[1,2,4],tomentionafew).Butlittleattentionhasbeenpaidsofartomergethesetwoimportantareasofresearch(see[7,21]).Inthispaper,weshallputemphasisinsuchaneco-epidemiologicalsystem.Weconsiderathreespecieseco-epide
5、miologicalsystem,namely,soundprey(suscep-tible),infectedprey(infective)andpredator.Weconsiderthecasewhenthepredatormainlyeatstheinfectedprey.ThisisinaccordancewithapreviousmodelbyHadelerandFreedman[7]whichdescribesapredator-preymodelwherethepreyisinfectedbyaparasite,andthepr
6、eyinturninfectsthepredatorwiththatparasite.Theinfec-tionweakensthepreyandincreasesitssusceptibilitytopredation,whilenopredatorimpairinge ectisaccountedfor.Whilethepaperismainlytheoreticalanddoesnotaddressanyspeci csituation,thereadermay ndseveralexamplesin[7].Wede-rivepersis
7、tenceandextinctionconditionsofthepopulationsandwealsodetermineconditionsforwhichthesystementersaHopf-typebifurcation.Moreover,weobservethatthebifurcatedbranchesaresupercriticalinsomeparametricregionspaceinaspecialcasewhenthepredatorresponsefunctionisaHolling-typeIIfunction.0
8、362-546X/99/$19.00?1999ElsevierScienceLtd.Allrightsreserved.PII:S0362-546X(
