a singular perturbation method 4 saddle connections90smithp19scan外语英文电子书

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1、REVISTAMATEMATICAdelaUniversidadComplutensedeMadridVolumen3,número1,990.Asingularperturbationmethodforsaddleconnectionsandsubharmoníesofcertainnonlineard~fferentialequationswithfixedsaddlepointsPETERSMITHABSTRACT.Saddleconnectionsandsubharmonicsareinves

2、tigatedforaclassofforcedsecondorderdifferentia¡equationswhichhaVeafixedsadd¡epoint.Intiteseequations,whichhavelineardampingandanonlinearrestoringterm,titeamp¡itudeoftheforcingterrndependsondisplacemeníintitesystem.Sadd¡econnectionsaresignificantinnonlin

3、earsystemssincetheirappearancesignalsahomoc¡inicbifurca-tion.Titeapproachusesasingularperturbationasetitodwhichhasafair¡ybroadapp¡icationtosaddleconnectionsandalsotoVarioussubharmonics.Thesingularperturbationisunusualinthatitusesatime-sca¡ewhichhastobec

4、onstructedoveraninflniteinterVal.ThesystemwithacubierestoringtermandaquadraticamplitudeisIookedatinsornedetai¡.1.INTRODUCTIONPorcertainnon¡ineardifferentia¡equationsitomoclinicbifurcationoccurswitentitesiableandunstablemanifoldsofasaddlepointoftitesyste

5、miníersecítituscreatingwitatisknownasaitomoc¡inicsaddleconnection.Probablytitemostwidelyinvestigateddifferentialequationwiticitexitibitsitomochinicbifurcation,perioddoublingandsirangeattractorsisDuffing’sequationwititlineardamping,cubicrestoringforceand

6、harmonicforcing.TitequalitativebeitaviourofsohutionsoftitisequationisnowwellunderstoodandacompreitensiveaccountoftitesubjectcanbefoundintitetextbyGuckeniteimerandHolmes[6].TitereviewbyGreenspanandHolmes[5]andtitebookbyTitompsonandStewart[¡3]containfurti

7、terbackgroundmaterialre¡evanttotitesubjectoftitispaper.InDuffing’sequationtitesaddhepointisassociaíedwitittitePoincarémapoftitefixedpointofanunstableperiodicso¡ution.Titelocationoftitisfixedpointvanesintheparameterspaceoftitesystem.Fromtitepointofviewof

8、applyingperturbationprocedurestitereisconsiderabheinsigitttobegainedby1980MathematicsSubjectClassification(1985revision):34D15,581<22.EditorialdelaUniversidadComplutense.Madrid,1990.90P.Smithinvesíigatingrnode¡syswrnswitichitavef