常微分方程規(guī)范形若干問(wèn)題的研究.pdf

1、⑧天庠大獸碩士學(xué)位論文_K一；ill■踵爿置躅irll■■們0學(xué)科專業(yè)：工程力學(xué)作者姓名：胡蘭霞指導(dǎo)教師：張琪昌教授r油出Z“rr六斗R堂2005年1月ABSTRACTNormalformtheoryplaysanimportantroleinthestudyofthedynamicalbehaviorofnonlinearsystemsneartheequilibriumpoint，becauseitCaD_simplifythean

2、alysisandformulationsSothenormalformCanbeusedconvenientlyforanalyzingthedynamicalbehavioroftheoriginalsysteminthevicinityofthecriticalequilibriumHoweverthenormalformisnotuniqueduetotheuncertaintyofthecomplementaryspaceof

3、linearoperatoraccordingasclassicalnormalformtheoryThesimplestnormalformisbaseonmatrixtheorymadnonlineartransformation，byemployingthenearidentitynonlineartransformationstomaketheoriginaldifferentialequationsortheclassical

4、normalformtObesimplifiedThispaperintroducesthedifferencebetweenclassicalnormalformandthesimplestnormalform；furthermore，theHopfbifurcationsystemandnonresonancedoubleHopfbifurcationsystemarestudiedaccordingasthemethodofthe

5、simplestnormalformHoweveritisnotasimpletasktocalculatethenormalformforagivensystemofdifferentiaIequationTherearethreebasicmethodstocalculatethenormalfc)rm：matrixrepresentationmethod，adjointoperatormethod，andtherepresenta

6、tiontheoryofsl(2，R)，butallthesemethodsneedtheprofoundmathematicknowledge，andfurthermore，normalformtheoryanditsapplicationaredevelopingtothesimplestandhigh—dimension，calculatingthecoefficientsofthenormalformbecomemorecomp

7、licatedSotheassistantcalculationusingcomputerismoreandmoreimportant，anditisnecessarytodesigncomputerprogramwithgreatefficiencyJustaccordingasthispoint，softwaredevelopmentisincludedinthispaperThecomputerprogramofthesimple

8、stnormalformofHopfbifurcationsystemandnonsemisimpledynamicalsystemaredesignedTheresearchofthenormalformbecomeseasybyusingtheseprograms，SOthedynamicscharacteristicsofthecomplicatedhighdimensionnon—lineardynamicsystemsCanb