平面動(dòng)力系統(tǒng)極限集的新性質(zhì).pdf

1、安徽大學(xué)碩士學(xué)位論文平面動(dòng)力系統(tǒng)極限集的新性質(zhì)姓名：楊蕓申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：肖箭201004IIABSTRACTInthispaperweconsiderthepropertiesoftheomegalimitsetofaplanarsystem，usingthestabilityofanequilibriumthegeneralnatureoftheplanedynamicsystemtheintroductio

2、nofaDulacfunctionpositive(negative)invariantsetconstructedgiventhestateoftheωlimitsetαlimitset.westudythePoincarBendixsontheemobtainthefollowingsomeresultstheseresultsarenews.Theem2.3.1Iftheequilibriumpointofthesystem(1.

3、1.1)keepsyQxP????havingthesamesignthenthelimitsetofthesemibitwithintheboundregioncouldonlybeoneofthefollowingtwotypes(1)asingleequilibriumset(2)aclosedbit.Theem3.2.1Ftheplanesystem(1.1.1)Letsimpleconnectedregion()VV???∈Ω

4、∈Ωin()VV?，()11divVPVQ??()VV?equalstozeroinanysubdomaintheequilibriumof(1.1.1)isnotequaltozerothenfanynonequilibriumpointthelimitsetofPthere(a)If()()pVVω??then()pωisasinglepointsetemptyset(b)if()()()pVpVωφωφ?∩?≠∩?≠then()p

5、Vω∩?consistofsingularpoint.Theem3.2.2Ftheplanesystem(1.1.1)Letsimpleconnectedregion()VV???∈Ω∈Ωin()VV?，()11divVPVQ??()VV?equalstozeroinanysubdomaintheequilibriumof(1.1.1)isnotequaltozerothenfanynonequilibriumpointthelimit

6、setofPthere(a)If()()pVVω??then()pωisasinglepointsetemptyset(b)if()()()pVpVωφωφ?∩?≠∩?≠then()pVω∩?consistofsingularpoint.Thepaperisdividedintothreechapters.Thefirstchapterweintroducethebackgroundthevalueofstudyingthispaper