PERMANENCE AND PERIODIC SOLUTION OF NONAUTONOMOUS DELAY LOTKA-VOLTERRA DIFFUSION SYSTEM

1.IntroductionTheinfluenceofdiffusiononsystemdynamicalbehaviorhasbeenanAnportatsubjectofpopulationbiology.Morerealisticmodelsshouldincludesomeoftheststesofthesesystem,thatis,arealsystemshouldbemodeledbydmerelltialequationswithtimedelays.Kuanglllconsideredthepermanenceandpositiveperiodicsolutionofn-dimensionaldelayLotka-Volterracooperatesystem.Xiaoandafl2]discussedthepermanenceandpositiveperiodicsolutionofnonautonomous~ionLotforVolterracompetitivesystemsi.e.nit(t)=acfbi(t)--Zal,(t)xt] ZDti(…     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

1.IntroductionGopalsamyandLadajs[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,T20.Ifa>0,b<0andc=0,then(1.1)reducestotheLogisticequation.Ifb>0,(l.1)exhibitstheso--calledAlic...     

GLOBAL ATTRACTIVITY OF POPULATIONMODELS WITH DELAYS AND DIFFUSION

In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

STABLE POSITIVE PERIODIC SOLUTIONS OF THE PERIODIC COMPETITIVE SYSTEMS

ＳＴＡＢＬＥＰＯＳＩＴＩＶＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＴＨＥＰＥＲＩＯＤＩＣＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＳＬＩＨｕａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＸｉｄｉａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｉｎａ）ＣＨＥ...     

GLOBAL ASYMPTOTIC STABILITY IN A NONAUTONOMOUS COOPERATIVE SYSTEM

In this papert we consider the asymptotic behavior of a nonautonomous co-operative system. A sufficient condition is obtained for the existence of a unique globallyasymptotically stable strictly positive periodic solution for the nonautonomous systemwhen it is ω-periodic (ω>0).     

PERSISTENCE IN A THREE SPECIES LOTKA-VOLTERRA PERIODIC PREDATOR-PREY SYSTEM

ＰＥＲＳＩＳＴＥＮＣＥＩＮＡＴＨＲＥＥＳＰＥＣＩＥＳＬＯＴＫＡ－ＶＯＬＴＥＲＲＡＰＥＲＩＯＤＩＣＰＲＥＤＡＴＯＲ－ＰＲＥＹＳＹＳＴＥＭＣＨＥＮＬａｎｓｕｎ；ＰＥＮＧＱｉｕｌｉａｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎ...     

PERIODIC SOLUTIONS AND PERIOD-SIMILARITY OF A GROWTH MODEL WITH AGE-STRUCTURED POPULATION

The present paper deals with the periodic behaviours of an age-structured populationmodel.The period-similarity is proposed,which reveals a certain similar structure between thosepopulation models with distinct age structure.In addition,other results show that the fluctuations ofan age-structured population are closely related with the age structure.     

SOLITON AND ELLIPTICAL PERIODIC SOLUTIONS TO THE MODIFIED NONLINEAR SCHRODINGER EQUATION

1.IntroductionAsiswellknown,theNLSE.02 ac Iql:q=0(1)'N Zap Iql:q=0(1)describesthepropagationofpicosecondOPticalpulseinamonomodeOPticalfiber,whereq(',T)istocomplexpulse,'represelltsthedistancealongthedirectionofpropagation,Trepresentsthetimeinthegroupvelocityframeandrs=11.TheNLSEhasbrightsolitonsolutionwhend==1,anddarksolitonsolutionwhena=11.Inthisnotewehaveobtainedthedarksolitonsolutionwhena~1.However,recentworkshaveshownthattheNLSEisnotsufficieDttodescribethepropagationoffemtosecond…     

A NEW PROOF OF THE HADAMARD MONODROMY THEOREM AND THE PERIODIC SOLUTION FOR A CLASS OF O.D.E.SYSTEMS AT RESONANCE

Early in 1904,Hadamard[1]showed the scale implicit function theorem of finitedimensions.Then it was generalized to infinite dimensions.In this paper a new proof of this theoremis given and the unique existence of the periodic solution for a class of ordinary differential equationsystems at resonance is obtained.     

UNIFORM PERSISTENCE IN DISCRETE SEMIDYNAMICAL SYSTEM AND ITS APPLICATION

ＵＮＩＦＯＲＭＰＥＲＳＩＳＴＥＮＣＥＩＮＤＩＳＣＲＥＴＥＳＥＭＩＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮ￥ＷＡＮＧＷｅｎｄｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，...     

UNIFORM PERSISTENCE AND GLOBAL ATTRACTIVITY FOR NONAUTONOMOUS COMPETITIVE SYSTEMS WITH DISPERSION

In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse between the two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system. Furthermore, we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.     

A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS

In this paper,we prove the existence of multiple periodic solutionsfor a class of singular Hamiltonian systems with sublinear terms via variationalmethods.     

ANALYSIS OF TWO-MACHINE CONWIP SYSTEM: MATRIX GEOMETRIC SOLUTION

1. IntroductionIn the past decade, various pull controlled production systems have received much attentionalong with the influence of Japanese manufacturing techniques. Pull systems are motivatedby the concept of just-in-time(JIT) whose objective is that material should be produced onlywhen it is needed, and only in the quantities needed. The most typical pull systems are Kanban(Japanese for card) systems(see e.g., [l--gi) and CONWIP (constant work--in-process) systems(see e.g., [1], [10]…     

LOCAL AND GLOBAL BIFURCATIONS AND APPLICATIONS IN A PREDATOR-PREY SYSTEM WITH SEVERAL PARAMETERS

A predator-prey system,depending on several parameters,is investigated forbifurcation of equilibria,Hopf bifurcation,global bifurcation occurring saddle connection,and global existence and nonexistence of limit cycles,and changes of the topological structureof trajectory as parameters are varied.     

UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES COOPERATIVE SYSTEM WITH TIME DELAYS

ＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＩＮＮ－ＳＰＥＣＩＥＳＣＯＯＰＥＲＡＴＩＶＥＳＹＳＴＥＭＷＩＴＨＴＩＭＥＤＥＬＡＹＳ￥ＣＵＩＪｉｎｇ＇ａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍ...     

TIME-DEPENDENT COOPERATIVE SYSTEM OF POPULATION GROWTH

*ThisresearchissupportedbytheNationalNaturalScienceFOundationofChina.1.IntroductionThevastmajorityofmathematicalmodelswhichhavebeenusedintheoreticalecologytostudythedynamicsofpopulationgrowthareautonomous.Thatistosaystheyattempttodescribethegrowthandinteractionofspecieswithconstantvitalparameterslivinginaconstantenvironment.Whilethishypothesisofconstantenvironmentandvitalparametersisjustifiableundersomecircumstances,amorerealisticmodelwouldcertainlyallowforthetemporalvariationoftheseparamet…     

GLOBAL AND LOCAL BIFURCATION IN PERTURBATIONS OF NON－SYMMETRY AND SYMMETRY OF HAMILTONIAN SYSTEM

ＧＬＯＢＡＬＡＮＤＬＯＣＡＬＢＩＦＵＲＣＡＴＩＯＮＩＮＰＥＲＴＵＲＢＡＴＩＯＮＳＯＦＮＯＮ－ＳＹＭＭＥＴＲＹＡＮＤＳＹＭＭＥＴＲＹＯＦＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭ￥ＬＩＵＺｈｅｎｇｒｏｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉ...