IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

IntroductionInpractice ,thereexistmanyexamplesofimpulsivecontrolsystems (seeRefs.[1 ,2 ,3 ] ) .Recently ,impulsivecontrolhasbeenwidelyusedtostabilizeandsynchronizechaoticsystems(seeRefs.[4～ 1 5] ) .Forexample,thepredictivePoincarecontrol[4 ]andtheoccasionalproportionalfeedbackcontrol[5 ]aretwoimpulsivecontrolschemeswithvaryingimpulsiveintervals.Yangetal.inRefs.[7,1 1 ]studied ,respectively ,thestabilizationandsynchronizationofaclassofchaoticsystemscalledLorenzsystems .YangandChuainRef.[1 …     

Existence of time periodic solutions for a damped generalized coupled nonlinear wave equations

IntroductionInRef.[1 ] ,theauthorsestablishedtheuniqueexistenceofthesmoothsolutionforthefollowingcouplednonlinearequationsut=uxxx+buux+ 2vvx, (1 )vt=2 (uv) x. (2 )Thesewereproposedtodescribetheinteractionprocessofinternallongwaves.InRef.[2 ] ,ItoM .proposedarecursionoperatorbywhichheinferredthatEqs.(1 )and (2 )possesinfinitelymanysymmetriesandconstantsofmotion .InRef.[3 ] ,P .F .HeestablishedtheexistenceofasmoothsolutiontothesystemofcouplednonlinearKdVequation[4 ]ut=a(uxxx+buux) + 2bvvx,(…     

LAMINAR DISSIPATIVE FLOW IN A POROUS CHANNEL BOUNDED BY ISOTHERMAL PARALLEL PLATES

IntroductionTheproblemofforcedconvectioninaporousmediumchannelorductisaclassicalone (atleastforthecaseofslugflow (Darcymodel) .Therehasrecentlybeenrenewedinterestintheproblembecauseoftheuseofhyperporousmediainthecoolingofelectronicequipment.Recently ,NieldandBejan[1]refertomorethan 3 0papersonthetopic ,butnoneofthemdealsexplicitlywiththecaseofthermaldevelopment.ThisgapintheliteraturehasbeenpartlyfilledbyNieldetal.[2 - 4 ].Lahjomrietal.[5 ,6 ]havesolvedmathematicallysimilarproblemsbyusingthe…     

Maximum principles for generalized solutions of quasi-linear elliptic equations

1　IntroductionandMainRrsultsSincethe 1 950s,therehasbeenarapidprogressinthestudyoftheregularitytheoryforgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceformwithseveralvariables,whichhasplayedanimportantroleinthestudyofquasi_linearequations (seeRefs.[1 ,2 ] ) .But,inspiteofthefactthatMorry[3 ]provedtheFredholmAlternativetheoremwithrespecttotheexistenceofgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceform (whichisageneralizationoftheclassicaltheory)a…     

Denoising method based on singular spectrum analysis and its applications in calculation of maximal liapunov exponent

IntroductionSingularSpectrumAnalysis (SSA)asadataanalysismethodhasbeenusedforyearsindigitalsignalprocessing .BroomheadandKing[1]proposedtheapplicationofSSAindynamicalsystemstheories.Vautardetal.[2 ,3]studiedthetheoryandapplicationofSSAindetail.AnalgorithmbasedonSSAisproposedtodenoisechaoticdatainthispaper.Theessenceofthisalgorithmistochooseproperorderofempiricalorthogonalfunctions (EOFs)andprincipalcomponents (PCs)toreconstructthesignal.ThefirstalgorithmtoestimatethemaximalLiapunovex…     

Shift of shock position for a class of nonlinear singularly perturbed problems

Thenonlinearsingularlyperturbedproblemisaveryattentiveobjectofstudyintheinternationalacademiccircles[1].Recently ,manyscholarsstudiedagreatdealofwork .Forexample,Boh啨[2 ],ButuzovandSmurov[3],O’Malley ,Jr.[4 ],Butuzov ,NefedovandSchneider[5 ]andKelley[6 ]andsoon .TheauthorconsideredaclassofsingularlyperturbednonlinearboundaryvalueproblemsfortheordinarydifferentialequationinRefs .[7～ 1 0 ] ,reactiondiffusionequationsinRefs.[1 1～ 1 3 ] ,singularlyperturbedproblemswithnonlocalboundarycond…     

COARSE-MESH-ACCURACY IMPROVEMENT OF BILINEAR Q4-PLANE ELEMENT BY THE COMBINED HYBRID FINITE ELEMENT METHOD

IntroductionByadding‘nodeless’incompatiblebubblemodesandpreservinggeometriccharacteristicofthevariationalprincipleinmechanics,thecombinedhybridmethod[1～4 ]remarkablelyenhancedcoarse_mesh_accuracyofconventionalquadrilateralelementsoflowerorder.ThequadrilateralplaneelasticelementCH(0_1 )proposedinRef.[3 ]isasuccessfulexample.Followingthegeometricpointofviewinmechanicscombinedwithmathematicalanalysis,anovelexpressionofthecombinedhybridvariationalprincipleisintroducedtoclarifyitsintrinsicmecha…     

REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

IntroductionAsanimportantnumericalmethod ,BoundaryElementMethod (BEM)hasbeenappliedinmanyareas[1].However,theBEMhasthedifficultiesofcalculatingsingularintegralsatnodesonboundaryoratinteriorpointsveryclosetotheboundary .TheaccuracyoftheBEMdependsontheprecisionofthecalculatedvaluesofthesingularintegrals,toagreatdegree.Manyresearchersdevotethemselvestothetreatmentofthesingularintegrals[2～3],whicharereviewedindetailbyRef.[4] .Ageneralregularizationalgorithmofevaluatingthephysicalquantitiesa…     

MODEL SHIFT AND STRANGE ATTRACTOR ON MBIUS STRIP

IntroductionIn 196 7,thewell_knownhorseshoemodelwasgivenbySmale,anditsinterestingdynamicalpropertieshadbeensuccessfullydescribedbytheshiftmappingonthesymbolicspace[1] .Sincethenthesymbolicdynamicalsystemshavebeenwidelystudiedandmanycomplexself_mappingshavebeenfoundtopossesssubsystem (X ,f)thatistopologicallyconjugatewith(Σ ,σ) ,whereΣisarelevantsymbolicspaceandσistheshiftmappingonΣ .Nevertheless,theself_mappingonsymbolicspaceismorethanshiftmapping (includingfinitesubshift) .Refs .[2 ]and…     

Existence of solutions for nonlinear elliptic boundary value problems

IntroductionInRef.[1 ]KannanandLockergivetheexistenceofatleastonesolutionofTy-h(t,y ,… ,y(n- 1) )y=f(t,y ,… ,y(n- 1) )　　 (a相似文献   

NONLINEAR STABILITY FOR EADY＇S MODEL

IntroductionEady’smodelisanimportantexampleof 3_dimensionalcontinuouslystratifiledquasi_geostrophicmotion[1].Recently ,someresultsofnonlinearstabilityforEady’smodelwereobtained[2 ,3],wheretheresultofRef.[3 ]istheimprovementofRef.[2 ] ,suchthattheresultisthebestinsomesense[4 ].Inthispaper,theresultofRef.[3 ]isimprovedbyestablishinganenhancedPoincar啨ｔｙｐｅｉｎｔｅｇｒａｌｉｎｅｑｕａｌｉｔｙ .ThenewresultshowsthatthenecessaryandsufficientlinearstabilityconditionforEady’smodelisalsothesu…     

NONLINEAR STABILITY FOR EADY'S MODEL

IntroductionEady’smodelisanimportantexampleof 3_dimensionalcontinuouslystratifiledquasi_geostrophicmotion[1].Recently ,someresultsofnonlinearstabilityforEady’smodelwereobtained[2 ,3],wheretheresultofRef.[3 ]istheimprovementofRef.[2 ] ,suchthattheresultisthebestinsomesense[4 ].Inthispaper,theresultofRef.[3 ]isimprovedbyestablishinganenhancedPoincar啨ｔｙｐｅｉｎｔｅｇｒａｌｉｎｅｑｕａｌｉｔｙ .ThenewresultshowsthatthenecessaryandsufficientlinearstabilityconditionforEady’smodelisalsothesu…     

Twisted bifurcations and stability of homoclinic loop with higher dimensions

1　IntroductionandHypothesesInrecentyears,withthedevelopmentofnonlinearsciencesandthedeepstudyofchaoticphenomena,thebifurcationproblemsofhomoclinicloopsforhigherdimensionalsystemswerestudiedextensivelyandalotofresultswereobtained (seeRefs.[1～ 8] ) .Especially ,Refs.[3 ,4]discussedthehomoclinicloopbifurcationswithcodimension 2 .Refs.[5,6]consideredthedegeneratedhomoclinicbifurcations.Inthispaper,westudythebifurcationsoftwistedhomoclinicloopsandthestabilityinhigherdimensionalspace .Considerth…     

Periodic solutions in one-dimensional coupled map lattices

IntroductionDynamicsofcoupledmaplattices (CML )haverecentlyattractedconsiderableattention[1- 4].IthasbeenfoundthatCMLsexhibitavarietyofspace_timepatterns:space_timeintermittency ,spatiotemporalchaos,frontsandinterfaces,nonlinearperiodicsolutions.Inthispaper,anone_dimensionalinfinitechainofnonlinearcoupledmapsisconsideredandtheexistenceofperiodicsolutionsisprovedwhenthecouplingstrengthαissmallenough .Ourapproachistheanti_integrablelimitintroducedinRefs.[5-7] .Intheanti_integrablelimit(coup…     

VISCO-ELASTIC SYSTEMS UNDER BOTH DETERMINISTIC AND BOUND RANDOM PARAMETRIC EXCITATION

IntroductionThestudyofrandomparametricexcitedsystemsisimportantintheengineeringsystems,andistheoreticallymoredifficultespeciallywhentheexcitationsarenarrow_bandrandomprocessesandparametricexcitedsystems.Inthecasewhenthesystemsareexcitedbycombineddeterministicharmonicandwide_bandprocesses,StratonovitchandRomanovskii[1] ,Dimentbergetal.[2 ] ,andNamachchivaya[3 ] usingthemethodofrandomaveragingandthemethodofKhasminskiiinvestigatedthealmostcertainstabilityofthesystems.AriaratnamandTam[4]discusse…     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

IntroductionThoughatransport_diffusion (orLagrange_Galerkin)method ,whichisalsocalledachar_acteristicsmethod ,isanoldone[1]andhasbeenextensivelyappliedtodealingwithPDEswithdiffusiontermand/orconvection ,ithadnotbeenmixedthefiniteelementmethodstotreatsuccessfullytheconvergenceofnumericalsolutionfortheNavier_Stokesequationsuntiltheearly198 0s[2 ].Intheearly 1 990s,Berm挷ｄｅｚｅｔａｌ.[3]appliedthismethodtodealingwiththeshallowwaterequationsonlyincludingthecurrentandthedepthofwaterandonlyderi…     

Nonlinear natural frequency of shallow conical shells with variable thickness

IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…     

EXPONENTIAL ATTRACTOR FOR THE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATION WITH DAMPING TERM

IntroductionAsymmetricversionofregularizedlongwaveSRLWequationsuxxt-ut =ρx uux, ( 1 )ρt ux =0 ( 2 )havebeenproposedasamodelforpropagationofweaklynonlinearionacousticandspace_chargewaves[1].Thehyperbolicsecantsquaredsolitarywavesolutions,thefourinvariantsandsomenumericalresultshavebeenobtainedinRef.[1 ] .Obviously ,eliminatingρfromEqs.( 1 )and( 2 ) ,wegetasymmetricregularizedlongwaveequation (SRLWE)utt-uxx 12 (u2 ) xt-uxxtt =0 . ( 3 )TheSRLWequation ( 3 )isexplicitlysymmetricinthexand…     

One-Dimensional Consolidation of Layered and Visco-Elastic Soils under Arbitrary Loading

ＩｎｔｒｏｄｕｃｔｉｏｎＡｆｔｅｒＴｅｒｚａｇｈｉ,ａｌｏｔｏｆｓｃｈｏｌａｒｓｈａｖｅｄｏｎｅｏｕｔｓｔａｎｄｉｎｇｒｅｓｅａｒｃｈｏｎｔｈｅｐｒｏｂｌｅｍｓｏｆｏｎｅ＿ｄｉｍｅｎｓｉｏｎａｌｃｏｎｓｏｌｉｄａｔｉｏｎ .Ｗｉｌｓｏｎ ( 1974) [1] ａｎｄＢａｌｉｇｈ( 1978) [2 ] ｅｔａｌ.ｈａｖｅｓｔｕｄｉｅｄｔｈｅｃｏｎｓｏｌｉｄａｔｉｏｎｕｎｄｅｒｔｈｅｒｅｃｔａｎｇｕｌａｒｌｏａｄｉｎｇ .Ｉｎ 1988,ＷＵｅｔａｌ.[3] ｗｏｒｋｅｄｏｕｔｔｈｅｇｅｎｅｒａｌｓｏｌｕｔｉｏｎｓｏｆｏｎｅ＿ｄｉｍｅｎ…     

Analysis of chebyshev pseudospectral method for multi-dimensional generalized srlw equations

IntroductionAsymmetricregularizedlongwaveequation (SRLWE) 2 x2 -1 u t = x ρ+ 12 u2 ,　 ρ t+ u x=0 (1 )hasbeeninvestigatedinRef.[1 ] .Thesystem (1 )ofequationsisshowntodescribeweaklynonlinearion_acousticwaveandspace_chargewaves.Thehuperbolicsecantsquaredsolitarywaves ,thefourconservationlaws,andsomenumericalresultshavebeenobtainedinRef.[1 ] .Obviously ,eliminatingρin (1 ) ,weobtainaclassofregularizedlongwaveequationutt-uxx+ 12 u2xt-uxxtt =0 . (2 )TheSRLWequationisexplicitlysymmetric…