一类非线性差分方程的持久性与全局吸引性

本文研究了差分方程ｘ（ｎ＋１）＝ｘｐｎｆ（ｘｎ，ｘ（ｎ－ｋ１），…，ｘ（ｎ－ｋｒ））的持久性与全局吸引性，解决了文［３］提出的两个研究课题，所得结果包含了文［３］的相应结果．     

GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION

In this paper the global attractivity of the nonlinear difference equation xn 1 = a bxn / A xn-k, n =0, 1, …，is investigated, where a, b, A ∈ (0, ∞), k is an positive integer and the initial conditions x- k, …，x- 1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].     

某类差分方程零解的全局吸引性及其应用

研究差分方程△xn=r n f(x n-k)的全局吸引性），用二次迭代法导出方程的零解全局吸引的一族新的充分条件，将结果应用于Logistic差分方程及Michelis-Menten差分模型，所得推论改进了已有结果。     

一类时滞微分方程平衡点的全局吸引性

利用相关的差分方程的全局吸引性研究了具时滞的单种群模型N(t)=r(t)N(t)1-N(t-τ)/1-cN(t-τ)的平衡点-x=1的全局吸引性,所获结果改进了文献中相关的结论.     

GLOBAL ATTRACTIVITY OF A DIFFERENCE EQUATION

In this paper,we investigate the global stability of all positive solutions to a difference equation.We show that the unique positive equilibrium of the equation is a global attractor with a basin under some certain conditions on the coefficient.     

ON THE GLOBAL ATTRACTIVITY FOR A NEUTRAL DIFFERENCE EQUATION WITH TWO DELAYS

ＯＮ　ＴＨＥ　ＧＬＯＢＡＬ　ＡＴＴＲＡＣＴＩＶＩＴＹ　ＦＯＲ　Ａ　ＮＥＵＴＲＡＬ　ＤＩＦＦＥＲＥＮＣＥ　ＥＱＵＡＴＩＯＮ　ＷＩＴＨ　ＴＷＯ　ＤＥＬＡＹＳＯＮＴＨＥＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＦＯＲＡＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴ...     

GLOBAL ATTRACTIVITY IN A DISCRETE MODEL OF NICHOLSON'S BLOWFLIES

ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＩＮＡＤＩＳＣＲＥＴＥＭＯＤＥＬＯＦ　ＮＩＣＨＯＬＳＯＮ＇Ｓ　ＢＬＯＷＦＬＩＥＳＬｉＪｉｎｇｗｅｎ（李经文）（ＳｈａｏｙａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ湖南邵阳师专,邮编;４２２０００）Ａｂｓｔｒａｃｔ：Ｃｏｎｓ...     

一类非线性变系数差分方程平衡点的全局吸引性

本利用相关的差分方程的全局吸引性研究了一类具时滞的非线性变系数差分方程ｘｎ＋１＝ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ１－ｃｘｎ－ｋ）的正平衡点ｘ＾－＝１的全局吸引性,获得了一个好的充分条件。     

一类非自治非线性时滞微分方程的全局吸引性

本文研究了非自治非线性时滞微分方程x‘(t)=r(t)(1 x(t))f(xt),t≥0，得到其零解全局吸引的一个充分条件，推广了[1]的方法。把结果应用于几类广义时滞Logistic方程，或得到了一些新的结果，或改进了一些已知结果。     

GLOBAL ATTRACTIVITY IN THE DISCRETE LASOTA-WAZEWSKA MODEL

§ 1　IntroductionConsider the delay difference equationNn 1 -Nn =-μNn pe- r Nn- k,　 n =0 ,1 ,2 ,... (1 )whereμ∈ (0 ,1 ) ,r,p∈ (0 ,∞ ) and k∈N,where N denotes the setofnonnegative integers.Equation(1 ) is a discrete analogue of the delay differential equationd N(t)dt =-μN(t) pe- r N(t-τ) ,　 t≥ 0 ,(2 )which was used firstby Wazewska-Czyzewska and Lasota[1 ] as a model for the survival ofred blood cells in an animal,see also[2 ] .Here N(t) denotes the number of red blood cellsat…     

血生成模型的全局吸引性

在本文中，我们进一步研究时滞微分方程它由Ｍａｃｋｅｙ和Ｌａｄａｓ［２］提出作为血生成模型．我们建立了（＊）的平衡是全局吸引子的新的充分条件，我们还改进了Ｇｏｐａｌｓａｍｙ，Ｋｕｌｅｎｏｖｉｃ和Ｌａｄａｓ［１］所得到的某些结果．     

EXISTENCE AND GLOBAL ATTRACTIVITY OF POSITIVE SOLUTIONS OF A NONAUTONOMOUS LOGISTIC TYPE MODEL WITH QUADRATIC NONLINEARITY

Consider the nonautonomous logistic modelwhere {pn} is a sequence of positive real numbers, {kn} is a sequence of non-negative integers satisfying We obtainnew sufficient conditions for the attractivity of the equilibrium x = x of the model. Our results improve ones which were established by Gapalsamy and Ladas recently, and solve some research projects posed by Kocic and Ladas in [7].     

一类非线性中立型差分方程的振动性(英文)

考虑一类非线性中立型差分方程Δ（ｘｎ － ｐｎｘｎ－ ｋ） ＋ ｑｎｆ（ｘｎ－ ｌ） ＝ ０ （）我们得到了其所有解振动的几个充分条件．     

PERIODIC SOLUTIONS FOR A CLASS OF DELAYED NONLINEAR DIFFERENCE EQUATIONS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,some sufficient conditions are established for the global existence of positive periodic solutions of a class of delayed nonlinear difference equations.     

GLOBAL ATTRACTIVITY IN A MODEL OF BOBWHITE QUAIL WITH DELAY

1IlltroductionInl99o,MiltinandB.lairl1]raisedadifferenceequationasapopulationmodelforthegrowthofthebobwhitequailpopulationofnorthernWisconsin.Inl994,Ladas,G.proposedthefollowingopenproblem[']:"(a)Investigatetheboundedness,persistence,permanence,oscillation,periodicity,andglobalattractivity;(b)ExtendEq.(*)byintroducingdelaysintothemodel,andinvestigatethedelayedequation.".Inl996,TangHeng-shengandOuChun-hua[3]considereditsglobalattrac-tivity,partlyansweredaboveopenproblem(a).Inl999,byintrodu…     

ATTRACTIVE BEHAVIOR OF SOLUTIONS OF A NONLINEAR HIGHER ORDER DIFFERENCE EQUATIONS

In this paper, we study the global attractivity of solutions of higher order nonlinear difference equation xn+1=f(xn+1-1,xn+1-2,…,xn,xn-1,)n=0,1,2,…, where f is a continuous, positive, decreasing function on [0,+∞)1+1\{(0,…,0)}. We extend some known global behavior of the solutions of nonlinear higher order difference equations.     

一类二阶非线性微分方程解的全局二分行为

本文讨论非周期二阶非线性微分方程：x“=f(t，x，x‘)解的全局二分行为，所得结果较好地改进和推广了关于周期方程的相应工作．     

一类时滞微分系统的周期解和全局吸引性

本文考虑如下时滞高维微分周期系统的周期解.利用重合度理论中的延拓定理和Lyapunov泛函方法讨论了上述系统周期解的存在性和全局吸引性,得到了便于应用的新结果.     

A LEAP FROG FINITE DIFFERENCE SCHEME FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS OF HIGHORDER

1.IntroductionItiswellknowthatthenonlinearequationsofSchr6dingertypeareofgreatimportancetophysicsandcanbeusedtodescribeextensivephysicalphenomenatll.InthispapergwewillconsidertheperiodicinitialvalueproblemforthefollowingclassofnonlinearSchrodingerequationofhighorder:wherem',MandMIareallpositiveconstant.Inthepaper[2])therehavediscussedinitialValueproblemofsystemsuchas(1.1)(1.3),introducedadifferenceschemeofconservationtype,andresearcheditsstabilityandconvergence.Otherwise,itisanimplicitmetho…     

GLOBAL ATTRACTIVITY OF THE HOPFIELD NEURAL NETWORKS

1 IntroductionHopfield neural networks is an associative memory model, it is also a neuraloptimization networks. This model has been studied extensively (see [1--12]).But in most of the literature, the signal function gi(x) is differentiable and isa sigmoid curve, and the sufficient conditions about the global attractivity ofthe Hopfield neural networks have no relevance to the delay. The aim of thispaper is to give a delayed sufficient condition of the global attractivity of theHopfield neur…