捕食模型和HIV模型的稳定性分析.pdf

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^}^2!3QualitativeanalysisofpreymodelandHIVmodelAbstractInthispaper,bycombiningofmathematicsandbiol

8、ogy,weestablishapredator-preymodelandusethetheoryofdifferentialequationstostudyit.ByanalyzingJacobiande-terminant,theLaSalleinvariantprinciple,usingsuitableLyapunovfunctionasandthecentermanifoldtheoryanddelaydifferentialtheory,wediscussthestabilityoftheequilib-riaandtheH

9、opfbifurcation,getseveralnewconclusionsandgeneralizethecorrespondingresultsintheliterature.InChapter1,wedealwithapredator-preymodelwithHollingtypeIIIfunctionalresponseincorporatingaconstantpreyrefuge:2xβ(x−m)yx˙=α(1−)−,k1+a(x−m)2(1.1.1)cβ(x−m)2yy˙=−dy+.1+a(x−m)2

10、Dependingontheconstantpreyrefugem,whichprovidesaconditionforprotectingmofpreyformpredationandbyanalysisthecharacteris