Sine-Gordon方程中混沌跳跃行为的机制

定性研究了Sine-Gordon方程在其广义近似惯性流形上的一个四维常微分方程。通过奇异扰动理论得到Silnikov同宿轨道存在的一个解析判定，然而在以往数值模拟中使用过的参数条件下，上面的判定不完全成立。于是进一步利用能量差方法，在这些参数条件下证明了至少存在四条结构稳定的脉冲轨道，它们正好反映了在Sine-Gordon方程的数值模拟中观察到 的混沌跳跃行为。     

WAVELET BASIS ANALYSIS IN PERTURBEDPERIODIC KdV EQUATION

I.IntroductionandSignsThephenomenaofnaturealwaysoccursatacertaintimeandacertainspace.Thecomplexityoftimeandspaceisduetodescribingtherelationbetweentimeandspaceandthelongtimebehaviorofsystembyusingthepartialdifferentialequation.Traditionally,thestatefunctionisexpandedinFotlrierseries,andthepartialdifferentialequationistransformedintotheordinarydifIYrentialequationwiththeevolutionofFouriercoefficientastimegoeson.ButitisverydifficulttoknowwelltheFouriercoefficientwhichplaysanimportantroleasthe…     

CONTROLLING HYPERCHAOS IN PLANAR SYSTEMS BY ADJUSTING PARAMETERS

IntroductionIn 1 990 ,Ott,GrebogiandYorke (OGY)introducedtheconceptofcontrolofchaosandgaveamethodforcontrollingchaos,knownastheOGYmethod[1].AfterOGY ,manyothermethodsforcontrollingchaoshavebeendeveloped[2 - 8].Otherrelatedtopics,suchasnoiseeffectsandoptimizationofthecontrol,havealsobeeninvestigated[9- 12 ].TheOGYmethodconsidersthemapξn+ 1=Fp(ξn) ,ξ∈R2 ,wherep∈Risaparameter,whichhasasaddleatacertainvalueoftheparameter.Thereforethereareaone_dimensionalstablemanifoldandaone_dimension…     

THE EXPONENTIAL ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION

In this paper, the exponential asgmptotic solution (E.A.S.) of differential equation is discussed. Firstly, E.A.S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E.A.S. are found out. Next, E.A.S. in matched asymptotic method is discussed. Finally, some examples are given.     

AN IMPROVEMENT AND PROOF OF OGY METHOD

I.IntroductionRecenhycontrollingchaosbecomesaninterestingsubject.In1990,E.Ott,C.GreogiandJ.A.Yorkelllgaveacollceptionofcontrollingchaos,andgaveacontrollingmethodknownasOGYmethod.ThereweremanyresultsthatshowedOGYmethodiseffective.AfterOGY,manymethodsofcontrollingchaosweregiven,mostofthemwerebasedonOGY13'4'5'6'71.SoOGYmethodisthefundamentofcontrollingchaos.ToachieveaproofofOGYisanimportanttaskformathematicstheoryofcontrollingchaos.Thispaperchangesthemethodofchoosingparameter,andprove…     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

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THE WILD SOLUTIONS OF THE INDUCED FORM UNDER THE SPLINE WAVELET BASIS IN WEAKLY DAMPED FORCED KdV EQUATION

I.IntroductionTheInethodtostudytheAIMbyusingthesplinewaveletbasisoriginatesfi.onl[l],adiscussiononthesoft'adjointtypenonlinearevolutionaryequations.However,itisstillaquestionwhetherthereexistsAIMonnonselfadjointtypenonlinearevolutiollaryequations.[2]l.esultsinthatthereexistsAIMbyusingtheFourierbasisinnonselftlcljointtype'sWDFKdVequatioll.[3]getstheAIMbyusillgthesplinewaveletbasisinperturbedperiodicKdVequation.[4]setsuptheglobalattractoranditsestimationoffractaldimensioninWDFKdVequati…     

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION

In this paper, starting from some fundamental properties of Heaviside function and δ-function, making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equation where M is an n -order linear differential operator, f(u) is a polynomial. By means of this method, we discuss some examples concretely. The results can be explained satisfac-torily in physics. If we deal with linear problem by this method, the result will agree with that drawn from theorem of impulse.     

Generalized synchronization of discrete systems

Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.     

AN EXAMPLE OF PDE WITH TWO ATTRACTORS

ＡＮＥＸＡＭＰＬＥＯＦＰＤＥＷＩＴＨＴＷＯＡＴＴＲＡＣＴＯＲＳＷａｎｇＧｕａｎｘｉａｎｇ（王冠香）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｓｕｚｈｏｕ２１５００６Ｐ．Ｒ．Ｃｈｉｎａ）ＸｕＺｈｅｎｙｕａｎ（徐...