非線性隨機(jī)參數(shù)系統(tǒng)的動(dòng)力學(xué)與控制研究.pdf

1、西北工業(yè)大學(xué)碩士學(xué)位論文非線性隨機(jī)參數(shù)系統(tǒng)的動(dòng)力學(xué)與控制研究姓名：張瑩申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：徐偉20070301西北工業(yè)大學(xué)碩七學(xué)位論文AbstractAbstractBifurcations，chaosanditscontrolinthestochasticnonlineardynamicalsystemswithrandomparameterareinvestigatedinthispaperThemaincon

2、tentsofthispaperareasfclllows：Inchapterone，theresearchingbackgroundofnonlineardynamicsismentionedAfterthat，thedevelopmenthistoryandthecurrentdevelopmentsofstochasticnonlineardynamicalsystemwithrandomparameterareintroduce

3、dhereFinallythereshowstheresearchingmethodsandthemaincontentsofthispaperInchaptertwo，thedynamicalbehaviorsofthestochasticdouble—periodbifurcationandthestochasticHopfbifurcationinthestochasticBonhoeffervanderPolsystemarcr

4、esearchedbytheChebyshevoahogonalpolynomialapproximationmethod，whichfirstlyreducesthestochasticnonlineardynamicalsystemintoitsequaldeterministicnonlineardynamicalsystem，thengeRingtheresultsbyusingtheeffectivenumericalmeth

5、odtothisequalsystemThenumericalresultsshowthatthestochasticbifurcationsinthestochasticBonhoeffervanderPolsystemarcbyandlargesimilartothatinthedeterministicBonhoeffervanderPolsystemButwiththeeffectoftherandomfactortherear

6、estillsomefeaturingdifferencesbetweenthemMeanwhile，theobtainedresultsshowthatChebyshevpolynomialapproximationisaneffectiveapproachtodynamicalproblemsinsometypicalnonlinearsystemswithboundedrandomparameterofanarch—likepro

7、babilitydensityfunctionInthechapterthree，usingthesameequaldeterministicsysteminthechaptertwo，thestochasticchaosinthestochasticsystemwiththerandomparameterisstudiedThenumericalresultsshowthatthechaosbehaviorinthestochasti

8、cBonhoeffervanderPolsystemisbyandlargesimilartothatinthedeterministicBonhoeffervanderPolsystemAfterward，thechaoticbehaviorsarecontrolledbybothnoisewhichisnonfeedbackcontrolmethodandtime—delayfeedbackcontrolmethodBecauseo

9、ftherandomfactortherearesomefuturesintheanalysisandcontrollingofchaosInthechapterfourthechaosbehaviorstheinDuffing—vanderPolsystemarediscussed，andthecontrollingofchaosbynoiseareresearchedtooInthelastchaptertheconclusions