三類微分方程解的性質(zhì).pdf

1、分類號(hào)密級(jí)學(xué)號(hào)題目■碩士學(xué)位論文三類微分方程解的性質(zhì)作者姓名一垡生鎏——指導(dǎo)教師姓名學(xué)科專業(yè)提交論文Et期陳斯養(yǎng)副教授應(yīng)用數(shù)學(xué)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