關(guān)于一維DAE的分類研究.pdf

1、長沙理工大學(xué)碩士學(xué)位論文關(guān)于一維DAE的分類研究姓名：劉加菊申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李兵20090401ABSTRACTSystemsofdifferentialalgebraicequations(DAEs)haVewideapplicationbackgrounds，andpowersystemscanbecharacterizedbyDAEsInthispapef，TheonedimensionDAEswitht

2、hespecialalgebraicpartwhichisoneofy“羅r。一，y2七1萬≯7andy(少”萬力(冊，七，，，甩∈Nand以≥2)isstudiedbyusingtheclassificationtheoremandthenomformtheoryofthebifurcationproblemswithtrivialsolutionDrZhiHuiYangresearchedtheclassincationoftheo

3、nedimensionDAEswithlowercodimension(Codim≤3)undertheG’requiValenceinhisDoctoralthesis，andthispapernotonlycontainssomeofsystemswithlowercodimension(Codim≤3)butalsoincludesanumberofsystemswithcodimensiongreaterthan3Forexam

4、ple，thecondimensionofg(石，y)is4wheng(x，y)isoneofy5融，y5萬砂andJ，2萬x5ThispaperwillbediVidedintofourchaptersInthe6rstchapterwebrieflyintroducethemainlyresearchesandstudytrendsofdifferential—algebraicequations(DAEs)andweintrodu

5、ceourresearchesandinnoVationsofthispaperInthesecondchapter，weintroducesomebasicconceptsandideasonsingularitytheoryofthebifurcationproblemsanddif6erentialalgebraicequations(DAEs)，includingGTequivalentietcThemainpartsarein

6、thethirdandfouthchapterInchapter3，wediscusstheclassificationoftheonedimensionDAEswiththespecialalgebraicpartwhichisoneofy”艿x2。一1andy2‘1萬z2‘(，，l，七，，∈N)underGTEquiValentInchapter4，wemakediscussiontheclassificationoftheoned