非线性对流系统的空间混沌行为

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1、山东大学硕士学位论文ABSTRACT2-Ddiscretedynamicalsystems，particularly2-Ddelayeddiscretedynamicalsystems，constituteanimportantpartofdelayedlarge—scalesystems，belongingtothefieldofmultivariablediscrete·timesequencesorspatialsequencesincontroltheory．Asapartof2-Ddiscretedynamicalsyst

2、ems，thenonlinear"convectionsystemisanewresearchfielddevelopedinrecentyears．Duetoitsimportanceinsolvingpracticalproblemsanditswide-rangedapplications，ithasbecomeanattractiveacademicresearchareainrecentyears．Inthisthesis，basicresearchiscarriedoutonspatialdynamicaltheory,

3、spatialchaos，andcontrolofnonlinearconvectionsystems．Themaincontentsofthethesisincludethefollowingaspects：ITheDefinitionofSpatialChaosintheSenseofRotationNumberIntervalBasedontheoverallanalysesof1-Ddiscretedynamicalsystems，aseriesofnewconceptsareintroducedreasonablyinth

4、espace，includingmappingcircle，rotationnumber,rotationnumberinterval，ashiftonthesequencespace，andSOon，SOthatwehavesomenewresearchworksdonewell．Forexample，basedontheconstructionofspatialkperiodicorbits，andthetheoremofrotationnumberintervalin2-Dnonlineardiscretedynamicals

5、ystems，qualitativeanalysisofboundarystabilityisstudied．Also，thebehaviorofspatialchaosinthesenseofrotationnumberintervalinnonlinearconvectionsystemsiSdiscussed．IIPerturbationControlonSpatialChaosFor2-Ddiscretedynamicalsystems，thecontrolofspatiallychaoticbehaviorsisinves

6、tigated，andtheperturbationcontrolonspatialchaosisstudied．Byextendingthemethodoftheperturbationcontrolappliedto1-Dsystemsto2-Ddiscretedynamicalsystems，westudyitscontrolonspatialchaosinthesenseofspace．Somesufficientconditionsonthestabilityofthefixedsurfacearealsoobtained

7、．IIIFeedbackControlonSpatialChaosFor2-Ddiscretedynamicalsystems，thecontrolofspatiallychaoticbehaviorsisinvestigated，andthedualitynonlinearfeedbackcontrolandprediction—basedm山东大学硕士学位论文feedbackcontrolofspatiallychaoticbehaviorsarealsostudied1．Themethodofdualitynonlinearf

8、eedbackcontrolovercomesthelimitationthattheconvergencecontroldistrictoftheperturbationcontrolissmall，difficulttoregul