17207.脈沖生態(tài)系統(tǒng)周期解的存在性

1、分類號學(xué)校代碼10542學(xué)號201202100859脈沖生態(tài)系統(tǒng)周期解的存在性ExistenceofPeriodicSolutionsforImpulsiveEcosystem碩士生姓名：陳昌榮指導(dǎo)教師姓名、職稱：李建利教授學(xué)科專業(yè)：應(yīng)用數(shù)學(xué)研究方向：常微分方程湖南師范大學(xué)學(xué)位評定委員會辦公室二零一五年五月ABSTRACTThetheoryofimpulsivedifferentialisoneofimportantbranchesof

2、differentialequationsandmathematicstheoryInthefieldofmodernappliedmathematics，ithasmadeconsiderableheadwayinrecentyears，becauseallthestructureofitsemergencehasdeeppaysicalbackgroundAsanimportantbranchofimpulsivedifferent

3、ialtheoryperiodicsolutionsandperiodicboundaryvalueproblemshavealwaysbeenaveryactivefieldwhichattractmanyscholars’researching，andhaveacquiredmanycopiousresultsThisthesisofMasteriscomposedofthreechapters，whichmailllystudie

4、dtheexistenceofperiodicsolutionfornonlinearimpulsivedifferentialcquationUsingtwomethods，oneisPoincar@mapmethod，anotherisbifurcationmethodInthefirstchapter，wefirstintroducethedevelopmentofimpulsivedifferentialtheoryandthe

5、latestadvancement，andstudysomeresultsofimpulsiveperiodicboundaryvalueproblems，whichgivenbysomeexpertsintheinnerandoutercountryInthesecondchapter，WediscussHollingIVpredatorpreysystemThesufficientconditionsofexistenceandst

6、abilityofsemitrivialsolutionandpositiveperiod—lsolutionareobtainedbyusingthePoincar6mapandanalogueofthePoincar6criterionInthethirdchapter，weusebifurcationmethodsresearchtheexistenceofperiodicsolutionfornonlinearHollingII

7、predatorpreysystemThroughtheS—tandardbifurcationtheorems，wecanoutofbranchesofsolutionsThenweusethehomotopyanalysismethod，wecangettheexistenceofperiodicsolutionInthelast，wemakeaconclusionofthispaperandgiveaplanofthefuture