帶有雙參量周期系統(tǒng)的周期解分支.pdf

1、學(xué)校代碼：10270分類號：0175.1學(xué)號：132200624碩士學(xué)位論文帶有雙參量周期系統(tǒng)的周期解分支學(xué)院：數(shù)理學(xué)院___________________專業(yè)：應(yīng)用數(shù)學(xué)_____________研究方向：常微分方程與動力系統(tǒng)研究生姓名：__________李雪麗______________指導(dǎo)教師：韓茂安教授___________完成日期2016年3月30日AbstractShanghaiNmalUniversityMasterof

2、PhilosophyAbstractThepurposeofthispaperistoinvestigatethebifurcationsonaclassofonedimensionalperiodicsystemswithasmallparameterafterperturbations.Accdingtothefirstderanalysisoftheperiodicsolutionsofperiodicdifferentialsy

3、stemwithasmallparameterweintroduceanothersmallparameterintherighthofthedifferentialequationsgivetheaveragingtheyoffirstderoftheperiodicsystemswithmultipleparameters.Furthermebystudyingtheexpansionsoftheaveragingfunctions

4、inasmallparameterwediscusstheboundsofthenumberoflimitcycleswhichbifurcatefromtheperiodicbitsoftheunperturbedsystems.Thisessayiscomposedofthefollowingthreechapters.InChapter1webrieflyintroducetheresearchbackgroundprelimin

5、arythemainresultsthemethodusedinthispaper.InChapter2weconsideranonedimensionalanalyticdifferentialequationwithmultiplesmallparameters&入ofthefm:dx=G(6xX)eFdOwhere0e《入《1GFareperiodicfunctionswithrespecttoO.Fe=0theunperturb

6、edsystemhasafamilyofperiodicbitsfsufficientlysmallparameter入.UsingsomeknownresultsrelatedtotheperiodicsystemwithasmallparameterwegivetheexpressionofthefirstderaveragingfunctionM(zA).Thenbystudyingtheexpansionsoftheaverag

7、ingfunctionM(zA)inAwederivethecrespondingexplicitexpressionsobtaintherelationshipbetweenthemtheboundofthenumberoflimitcycleswhichbifurcatefromtheperiodicbitsoftheunperturbeddifferentialequation.InChapter3asapplicationexa

8、mplesweinvestigatetwofamiliesofperiodicsystemswithmultiplesmallperturbations.Thefirstoneisaplanarpolynomialdifferentialsystemthesecondoneisandinaryanalyticdifferentialequationwithmultiplesmallparameters.Bytakingpropertra

9、nsfmationsthesystemsbecomethefmsofthesystemthatwehavestudiedinchapter2.ThenweapplytheobtainedresultsinChapter2toderivethecoefficientsintheexpingexpressionsofthebifurcationfunctionsinasmallparameter.Utilizingtherelationsh