PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

PERIODIC SOLUTION AND ALMOST PERIODIC SOLUTION OF NONAUTONOMOUS COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING

In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution and the existence, uniform asymptotic stability of almost periodic solution are obtained.     

一类具有非线性扩散和时滞的捕食系统的持续性与周期解

研究了一类具有非线性扩散和Beddington-Deangelis功能性反应,且同时具有连续时滞和离散时滞的非自治两食饵一捕食者系统,证明了在适当条件下该系统是一致持久的,并且得到了系统正周期解全局渐近稳定的充分条件.最后,给出一个例子以说明得到的结果.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF ALMOST PERIODIC SOLUTION TO A DELAYED DIFFERENTIAL EQUATION

A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

一类概周期时滞捕食-食饵系统的概周期解

本文讨论一类概周期时滞捕食－食饵系统的一致持久性,通过构造一个Ｌｉａｐｕｎｏｖ函数得到该系统有界解的唯一性,并且给出正概周期解的存在唯一性定理。     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。     

THE EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTION

By using the ordinary dichotomy and theory of stability,we study the nonli- near differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear diffe- rential equation.     

EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTION IN A LOGISTIC INTEGRODIFFERENTIAL EQUATION WITH FEEDBACK CONTROL

1IntroductionThelogisticequation([8],l12])isoneoftheelementaryandmathematicallysimplemodelsusedtodescribethetempora1evolutionofasinglespeciespopulationinaconstantenvironment,inwhichaand5arepositiveconstants;aisrelatedtothereproductionofthespecieswhilebisrelatedtothecapacityofenvironmenttosustainthepopu1ation.Itisknownthatsoltitionsof(1.1)aremonotonicfunctionsoftwithlimN(t)=tifN(o)>o.Ithasbeenfoundthatsuchamonotonict-ooconvergencetofheequilibriumisnotrealisticincertainlaboratorypopulationsinte…     

PERIODIC SOLUTIONS FOR A CLASS OF DEGENERATE NEUTRAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point method, discusses the problem of periodic solution for a class of degenerate neutral periodic system with delay, and obtains some sufficient conditions for the existence and uniqueness of periodic solution of the system, the result extends and improves some results of paper [1-2].     

人口动力学中一类含时滞周期反应—扩散方程的正周期解分歧

本文研究人口动力学中一类含时滞周期反应-扩散方程的正周期解问题;利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。     

具有脉冲和时滞的Logistic模型的持续生存和正周期解的全局吸引性(英文)

本文研究了具有脉冲和时滞效应的Logistic模型.利用脉冲微分方程的比较定理,BohlBrower不动点定理和Lyapunov函数法,获得了系统持续生存,正周期解存在、唯一以及全局吸引的充分条件.结果表明正周期解的全局吸引性与时滞有关.     

EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR HOPFIELD NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

This paper is to study the existence and attractivity of almost periodic solution for Hopfield-Type delay cellular neural networks(HDCNNs) with variable coefficientsby combining the theory of the exponential dichotomy and Lyapunov functionals method and combine with some analysis techniques. We obtain some sufficient conditions to ensure the networks to have a unique almost periodic solution, and all other solutions converge to this solution.     

GLOBAL ATTRACTIVITY IN AN ALMOST PERIODIC PREDATOR-PREY-MUTUALIST SYSTEM

In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient conditions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.     

A REMARK ON HOFER-ZEHNDER SYMPLECTIC CAPACITY IN SYMPLECTIC MANIFOLDS M×R~(2n)

ＡＲＥＭＡＲＫＯＮＨＯＦＥＲＺＥＨＮＤＥＲＳＹＭＰＬＥＣＴＩＣＣＡＰＡＣＩＴＹＩＮＳＹＭＰＬＥＣＴＩＣＭＡＮＩＦＯＬＤＳＭ×Ｒ２ｎＭＡＲＥＮＹＩＡｂｓｔｒａｃｔＴｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅＨｏｆｅｒＺｅｈｎｄｅｒｃａｐａｃｉｔｙａ...     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

In this paper, we establish the existence of a positive periodic solution for a periodic delay single species population growth model, and obtain sufficient conditions for the periodic solution to be globally attractive.     

二次微分系统的反射函数及其周期解

本文给出了二镒多项式微分系统具有满足特定关系式的反射函数和存在周期解的充要条件，以及在此条件下反射函数的具体表达式及周期解的稳定性态。     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A DELAYED PERIODIC PREDATOR-PREY MODEL OF IVLEV TYPE

A periodic coefficients predator-prey system of Ivlev type with both discrete and continuous time delay is investigated. A sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory.