25566.兩類多項(xiàng)式微分系統(tǒng)的極限環(huán)研究

1、兩類多項(xiàng)式微分系統(tǒng)的極限環(huán)研究Studiesonlimitcyclesfortwoclassesofpolynomialdifferentialsystems作者：魏雪梅Author：WeiXuemei指導(dǎo)教師：查塑墼一Supervisor：璺塾墮璺叢!!絲g專業(yè)：應(yīng)用數(shù)學(xué)學(xué)位：理學(xué)項(xiàng)士Degree：Mast，erofScience授予單位：浙江師蕉盤鱟Institute：—Z—hejiangNormalUniversity—May20

2、14AbstractThesecondpartofthefamous16thHilbertproblemasksforthemaximumnumberandrelativepositionsoflimitcyclesofplanarpolynomialvectorfieldsofagivendegree禮Thisproblem，openedformorethanacenturyhasmadealotofresultsHowever，it

3、isstillnotsolvedevenforn=2Inthispaper，basedontheaveragingmethodofbifurcationtheoryofdynamicalsystems，themaximumnumberandexpressionoflimitcyclesoftwoclassesofpolynomialdifferentialsystems&restudiedThefulltextofthecontenti

4、sdividedintothreechaptersThefirstchapteristhepreface，inwhichwemainlyintroducethebackgroundandknownresultsofthelimitcyclesofpolynomialdifferentialsystemsandbifurcation，andbrieflyillustratethemainworksofthethesisInthesecon

5、dchapter，weinvestigatethenumberoflimitcyclesofthegeneralizedLi6nardpolynomialdifferentialsystemsoftheform圣=Y一￡(911(。)fll(X)Y)一七￡2(夕12(x)f12(X)y)，17=一z—E(921@)，2l@)可hm(x)y2)一七￡2(922(x)丘2(z)yh22(x)y2)，for后=0and1respectivel

6、yWeprovidethemaximumnumberoflimitcyclesthattheabovedifferentialsystemscanhavebifurcatingfromtheperiodicorbitsofthelinearcenter圣=Y，17=XusingaveragingmethodoffirstandsecondorderThecontentsofthischapterimprovesrelatedresult

7、sin[36】Inthethirdchapter，theglobalshapeoflimitcyclesforthequinticpolynomialdifferentialsystems圣=Pl(z，Y)P5(z，y)，!)=QI(x，Y)Qs(x，可)，arestudiedMorepreciselybyusingtheaveragingmethod，weobtaintheapproximateexpressionsoflimitcy