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1、MathematicalModellingandAnalysisISSN:1392-6292(Print)1648-3510(Online)Journalhomepage:http://www.tandfonline.com/loi/tmma20PositiveSolutionsBifurcatingfromZeroSolutioninaPredator-PreyReaction–DiffusionSystemCun-Huazhang&Xiang-PingyanTocitethisarticle:Cun-Huazhang&X
2、iang-Pingyan(2011)PositiveSolutionsBifurcatingfromZeroSolutioninaPredator-PreyReaction–DiffusionSystem,MathematicalModellingandAnalysis,16:4,558-568,DOI:10.3846/13926292.2011.628707Tolinktothisarticle:http://dx.doi.org/10.3846/13926292.2011.628707Publishedonline:22
3、Nov2011.SubmityourarticletothisjournalArticleviews:292ViewrelatedarticlesFullTerms&Conditionsofaccessandusecanbefoundathttp://www.tandfonline.com/action/journalInformation?journalCode=tmma20Downloadby:[AcademyofMathematicsandSystemSciences]Date:21January2016,At:05:
4、12MathematicalModellingandAnalysisPublisher:Taylor&FrancisandVGTUVolume16Number4,December2011,558{568http://www.tandfonline.com/TMMAhttp://dx.doi.org/10.3846/13926292.2011.628707OnlineISSN:1648-3510cVilniusGediminasTechnicalUniversity,2011PrintISSN:1392-6292Positiv
5、eSolutionsBifurcatingfromZeroSolutioninaPredator-PreyReaction{Di usionSystemCun-HuaZhangandXiang-PingYanDepartmentofMathematics,LanzhouJiaotongUniversityLanzhou,Gansu730070,ChinaE-mail(corresp.):xpyan72@163.comReceived25May,2010;revised9July,2011;publishedonlineNo
6、vember1,2011Abstract.AnellipticsystemsubjecttothehomogeneousDirichletboundarycon-ditiondenotingthesteady-statesystemofatwo-speciespredator-preyreaction{di usionsystemwiththemodi edLeslie{GowerandHolling-typeIIschemesiscon-sidered.ByusingtheLyapunov{Schmidtreduction
7、method,thebifurcationofthepositivesolutionfromthetrivialsolutionisdemonstratedandtheapproximatedex-pressionsofthepositivesolutionsaroundthebifurcationpointarealsogivenaccord-ingtotheimplicitfunctiontheorem.Finally,byapplyingthelinearizedmethod,thestabilityofthebifu
8、rcatingpositivesolutionisalsoinvestigated.Theresultsobtainedinthepresentpaperimprovedtheexistingones.Keywords:predator-preyreaction{di usionsyste
