兩類傳染病模型與微生物培養(yǎng)模型的定性分析.pdf

1、大連理工大學碩士學位論文兩類傳染病模型與微生物培養(yǎng)模型的定性分析姓名：鐘鎮(zhèn)權(quán)申請學位級別：碩士專業(yè)：應(yīng)用數(shù)學指導(dǎo)教師：夏尊銓20081213兩類傳染病模型與微生物培養(yǎng)模型的定性分析QualitativeAnalysisofEpidemicTwoModelsandMicrobialCultureModelsAbstractBiologicdynamicsystemhasbeenallimportantborderbranchofbioma

2、thematicsfortheapplicationofthetheoryofdifferentialequationtobiologyInthisthesisforMSc，twoknownepidemicmodels，SISmodelandSEImodel，areimprovedundertheconditionofnonautonomous，suchthmtheimprovedmodelsarereflectingrealitybe

3、tterthanknownonesAndbasedonknowngeneralmathematicalmodelsofmicrobialculture，newmodels，reflectingrealitybetterwiththeincreasingratiobeingpositiveandtheyieldbeingalinearfunctionoraquadraticfunctionarepresentedStabilityanal

4、ysesfordifferentialequationsassociatedwithepidemicandmicrobialcontinuousculturemodels羽kmainresultsCanbesummarizedasfollows：1AnonamonomousepidemicSISmodelwithalleoefficientsbeingcontinuous，boundedCOperiodicfunctionsiSesta

5、blishedandanewsufficientconditionofexistenceanduniquenessofpositiveperiodicsolutionofthismodelispresented2AnonautonomousSEIinfectiOIlSmodelisestablished。Asufficientconditionfortheglobalasymptoticstabilityofthediseasefree

6、equilibriumisobtainedfromtransformingthemodelandconstructinganappropriateLiapunovfunctionForthesystems、析tllallcoefficientsbeing∞periodicfunctions，itfollowsfromemployingtheBrowertheoremof曩xedpo婦thatthesufficientconditions

7、forexistenceandtheglobalasymptoticstabilityofthepositiveperiodicsolutions3Amicrobialcontinuousculturemodelwithvariableyieldisestablishedundernewconditionsproposedinthisthesisbasedonaknownmathematicalmodelofmicrobialconti

8、nuouscultureFirstfortheyieldmodelbeingalinearfunction，thesystemdoesnotexistalimitcycleintheregion壤atisassertedfromconstructingtheBendixsonannularregionandaDulacfunctionandbyBendixson—Dulac’Sdistinguishingmethod，andfurthe

9、rmore，thesufficientandnecessaryconditionofglobalasymptoticstabilityofapositiveequilibrium弦婦lispresented。Second，fortheyieldmodelbeingaquadraticfunctionfromtransformingthemodel，asufficientconditionofexistingastablelimitcyc