三類微分方程解的性質.pdf

1、分類號密級學號題目■碩士學位論文三類微分方程解的性質作者姓名一垡生鎏——指導教師姓名學科專業(yè)提交論文Et期陳斯養(yǎng)副教授應用數(shù)學二oo六年四月THEPROPERTIESoFTHREECLASSESDIFFERENTIALEQUATIoNSHuahaiQiuAbstractThepropeitiesofthesolutionofdifferentialequationincludethestabilityoftheSOlution，osci

2、llationandpmiodieityandsoonthesepropertiesr“’ealthelong—termbehaviorofthedynamicalsystemsincealotofbiologicalregulaiandphenomenoninthebiologicalweredescribedbyusingdifferentialequations，whichdrewtheattentionofalotofexper

3、tsandscholarsandformedmanynewtopicsthathavestrongpracticalbackgroundweknowthatthestudyoftheco—exist，stability，oscillationotthespiceshasveryimportantpracticalmeaningtokeepecologicalequilibrationandprotectecologicalenviron

4、ment，eventosave、’aluableandrarebiologicswhichareonthevergeofbecomingextinctInthispaper，wediscussthepropertiesofthreeclassesofdifferentialequationsThepopulationdynamicssystemwhichAppliedcandescribe，calculateinordertoregul

5、ateandcontrolthedevelopmentalprocessesandthedevelopmentaltlendofspecies，whidlisoneofthemeticalbasisforpeopleexploitingresoulCeSmakioguseoflesoureesandprotectingresourcesInthep01)lclariondynamicsSystempeisistenceaJldgloba

6、llyasymptoticaIlystabilityisasubjectofgreattopicalinterest，Inthedocumentformerly，generally，conditionofthepersistenceisobtainedbyapplyingthecomparisontheorem”eobtainthegloballyasymptoticallystabilitybyusingLiapunovftmctio

7、nInthechapter2、u’econsider’apredator—preysystenlwithtimedelaymathematicalaual)’sesofsystemwithregardtothepositiveinvariantset，natmeofboundaryequilibriumbyusingchaIacteristicequationisalial3zedthesufficientconditionisobta

8、inedforlocallyasymptoticallystabilityofpositiveequilibriumw]lentimedelayrissmall，aadHopfbifurcationcanOccuraSthedelayincreasestor0Lastweobtaingloballyasymptoticallystabilityofboundaryequilibriumb3’applyinglocallyasymptot

9、ical])’stabilityandattractivenessandpersistencebyusinguniformrepdleltheorem，Thecorrectuessoftheconditionsofthetheoremisshownbyexampleandusing711atlabSOftwareGenerally，foraabstractfunctionaldifferentialequation，ifitsatisf

10、iessmileconditions，thenweCallgetaperiodicsolutionInthechapter3，webaseontheexistenceofperiodicsolution，usingthernethodoflineaxizationandapplyingthemeanvaluetheoremandthevariation—ofconstantsformula：wegetthesufficientcondi

11、tionoftheexponentialstabilityofperiodicsolutionofaclassofnonlinearfunctionaldifferentialsystemwegettheexponentialsl，abilityofaclassofperiodicLotkaVolterratypen—speciescompetitivesystemsInthelast50yearstheoscillationtheor