时滞捕食模型的稳定性与Hopf分支研究.pdf

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17、i•H“‰ŒÆa¬ÆØ©OnthestabilityandHopfbifurcationforpredator-preymodelswithtimedelaysAbstractTherearemanyfac

18、torsthataectthedevelopmentofspeciesinthenature,suchastime-delay,stage-structure,interactionbetweenspecies,patches,refuge,diseaseandsoon.Thesefactorsareimportanttothespecies.Inthispaper,weestablishexactpredator-preymodelsbasedontheabovefactorsandstudythestabilityandHopfbifurcationofthesemodels.Th

19、ispaperisdividedintofourchapters.Chapter1brie yintroducestheresearchedbackgroundofproblemsandthemainworkofthispaper.Chapter2studiesastage-structuredpredator-preymodelwithtimedelaysandpreda-torconsumingimmaturepreyonly.Byanalyzingthestage-structurepredator-preymodelandusingthestandardcomparisonthe

20、orem,sucientconditionsforpermanenceofthesystemarederived.Theexistenceandthelocallyasymptoticstabilityofnonnegativeequilibriaareconsideredwhichmadeusobtaintheimportantresultofthispaperthatthevariationofpredatorstagestr