简介：Inthispaper,westudytheperturbationofcertainofcubicsystem.Byusingthemethodofmulti-parameterperturbationtheoryandqualitativeanalysis,weinferthatthesystemunderconsiderationcanhavefivelimitcycles.

简介：我们与处理描述并且分析一个简单SIS模型。特别地，我们借助于asymptotically自治的系统的理论给完全质的分析。如果足够的接触率或能力是小的，向后的分叉发生，这被发现。在那里存在，也被发现双稳态地方性的equilibria。在导致疾病的死亡的情况中，向后的分叉也发生，这被显示出。而且，在一些条件，和潜水艇下面没有限制周期批评Hopf分叉发生在另外一个下面条件。

简介：Thispaperdealswiththebifurcationproblemsofmultiparameterandmultibranchandtheirapproximations.Itderivesgeneralapproximationresultsofsolutionbranchesintheneighbourhoodofasingular(limit,turningormultibranch)point,andshowsthatturningandmultibranchpointsarebifurcationpoints.TheabstracttheoriesareappliedtoamixedfiniteelementapproximationofstationaryNavier-Stokesequation.

简介：AnSMIBmodelinthepowersystems,especiallythatconceringtheeffectsofhardlimitsonbifurcations,chaosandstabilityisstudied.Parameterconditionsforbifurcationsandchaosintheabsenceofhardlimitsarecomparedwiththoseinthepresenceofhardlimits.Ithasbeenprovedthathardlimitscanaffectsystemstability.Wefindthat(1)hardlimitscanchangeunstableequilibriumintostableone;(2)hardlimitscanchangestabilityoflimitcyclesinducedbyHopfbifurcation;(3)persistenceofhardlimitscanstabilizedivergenttrajectorytoastableequilibriumorlimitcycle;(4)HopfbifurcationoccursbeforeSNbifurcation,sothesystemcollapsecanbecontrolledbeforeHopfbifurcationoccurs.Wealsofindthatsuitablelimitingvaluesofhardlimitscanenlargethefeasibilityregion.Theseresultsarebasedontheoreticalanalysisandnumericalsimulations,suchasconditionforSNBandHopfbifurcation,bifurcationdiagram,trajectories,Lyapunovexponent,Floquetmultipliers,dimensionofattractorandsoon.

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简介：轨道的分叉扭动有nonhyperbolicequilibria的homoclinic循环被调查。由在不受搅乱的homoclinic轨道附近构造本地坐标系统，PoincarHomoclinic轨道；周期的轨道；本地坐标系统；Poincar

简介：Inthispaper,westudythelocalbifurcationofcriticalperiodsnearthenondegeneratecenter(theorigin)ofaclassofLiénardequationswithdegree2n,andprovethatatmost2n-2criticalperiods(takenintoaccountmultiplicity)canbeproducedfromaweakcenteroffiniteorder.Wealsoprovethatitcanhaveexactly2n-2criticalperiodsneartheorigin.

简介：ＡＮＥＷＤＥＴＥＣＴＩＮＧＭＥＴＨＯＤＦＯＲＣＯＮＤＩＴＩＯＮＳＯＦＥＸＩＳＴＥＮＣＥＯＦＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＳＨＥＮＪＩＡＱＩ（沈家骐）；ＪＩＮＧＺＨＵＪＵＮ（井竹君）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎ...

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简介：Considerathree-dimensionalsystemhavinganinvariantsurface.Byusingbifurcationtechniquesandanalyzingthesolutionsofbifurcationequations,theauthorsstudythespacialbifurcationphenomenaofakmultipleclosedorbitintheinvariantsurface.Thesufficientconditionsoftheexistenceofmanyclosedorbitsbifurcatefromthekmultipleclosedorbitareobtained.

简介：在这篇论文，稳定性；有时间延期的小世界的网络的Hopf分叉被学习。由分析延期的变化，我们在马厩上获得几个足够的条件；不稳定的性质。当延期传递批评价值时，Hopf分叉可以出现。而且，方向；区分周期的答案的稳定性被正常形式理论调查；中心歧管减小。由数字模拟，最后，我们进一步在这篇论文说明定理的有效性。

简介：Thispaperstudiesaclassofquarticsystemwhichismoregeneralandrealisticthanthequarticaccompanyingsystem.x′=-y+ex+lx~2+mxy+ny~2,y′=x(1-Ay)(1+Cy~2),(*)whereC>0.Sufficientconditionsareobtainedfortheuniquenessoflimitcycleofsystem(*)andsomemorein-depthconclusionsuchasHopfbifurcation.

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简介：Inthispaper,thedynamicsofadelayedphytoplankton-zooplanktonmodelisconsidered.Takingthedelayduetothegestationofzooplanktonasparameter,wedescribethelocalHopfbifurcationbycentermanifoldtheoremandnormalform,thenwediscusstheglobalexistenceofperiodicsolution.Atlast,somesimulationsaregiventosupportourresult.

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简介：Inthispaperthedynamicsofaweaklynonlinearsystemsubjectedtocombinedparametricandexternalexcitationarediscussed.TheexistenceoftransversalhomoclinicorbitsresultinginchaoticdynamicsandbifurcationareestablishedbyusingtheaveragingmethodandMelnikovmethod.Numericalsimulationsarealsoprovidedtodemonstratethetheoreticalanalysis.

简介：Inthispaper,athreedimensionalratio-dependentchemostatmodelwithperiod-icallypulsedinputisconsidered.ByusingthediscretedynamicalsystemdeterminedbythestroboscopicmapandFloquettheorem,anexactperiodicsolutionwithpositiveconcentrationsofsubstrateandpredatorintheabsenceofpreyisobtained.Whenβislessthansomecriti-calvaluetheboundaryperiodicsolution(x_s(t),0,z_s(t))islocallystable,andwhenβislargerthanthecriticalvaluethereareperiodicoscillationsinsubstrate,preyandpredator.IncreasingtheimpulsiveperiodT,thesystemundergoesaseriesofperiod-doublingbifurcationleadingtochaos,whichimpliesthatthedynamicalbehaviorsoftheperiodicallypulsedratio-dependentpredator-preyecosystemareverycomplex.

简介：Inthispaperthebifurcationsolutionbranchesofasemi-linearellipticproblemarestudied,anditsextendedsystemsareconstructed.

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简介：Inthispaper,bifurcationofsmallamplitudelimitcyclesfromthedegenerateequilibriumofathree-dimensionalsystemisinvestigated.Firstly,themethodtocalculatethefocalvaluesatnilpotentcriticalpointoncentermanifoldisdiscussed.Thenanexampleisstudied,bycomputingthequasi-Lyapunovconstants,theexistenceofatleast4limitcyclesonthecentermanifoldisproved.Intermsofdegeneratesingularityinhigh-dimensionalsystems,ourworkisnew.