ON THE PERSISTENCE AND POSITIVE PERIODIC SOLUTION FOR PLANAR COMPETING LOTKA-VOLTERRA SYSTEMS

1IntroductionLetusa;onsi~~l'tile2-(1llTlellsiollalco'ttipetit;ion1,of-,ha--\./O]1,'lrra,s:\,s(t()lcfl.r]=.r,(l)j(t)--a,1(-t)xl--a,,(lt)x,),,.(II)ac=ac(6~(t-)--a21(t)x,--a22(t);rZ),xvhere(J:,.:x'2)eR;,~{(;t:l,.xZ)la:l20,IZ.20},l),(l),ail(t)fi{~j:lar(>conti…     

周期捕食与被捕食系统正周期解的稳定性

本文研究具周期系数的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ捕食与被捕食系统，建立了系统正周期解渐近稳定和全局稳定的新的判别准则。     

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.     

具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性

研究一类具有时滞和基于比率的三种群食物链捕食-被捕食动力学模型.证明了该系统在适当条件下的一致持久性;通过构造Lyapunov泛函,得到了该系统正平衡点全局渐近稳定的充分条件.     

具有捕食食饵种群的Chemostat模型的一致持续生存

本文主要讨论了单营养食物链的Chemostat模型的渐进性态,给出了该系统一致持续生存和绝灭的充分条件.     

PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

A three-species ratio-dependent predator-prey diffusion model with time de-lays is investigated. It is shown that the system is uniformly persistent under some ap-propriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.     

PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

有食饵补充的二维捕食食饵模型的周期解与概周期解

对于有食饵补充的非定常二维捕食食饵模型，利用微分不等式，讨论了周期解的存在性及其全局吸收性，概周期解的存在性及其在壳扰动不的稳定性。     

具有IV类功能反应的非自治捕食系统的持续性和周期解

本文讨论了一类具有HollingIV类功能反应的非自治捕食系统,利用Brouwer不动点定理和构造Liaponov函数的方法,得到该系统永久持续生存和存在唯一全局稳定的周期解的充分条件.     

一类捕食和被捕食系统的持久性

本文获得了一类捕食和被捕食系统持久性的充分条件 ,推广了文 [1]的部分结果     

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。     

PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM

In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.     

一个环境数学模型的一致持久性与稳定性

本文研究一个生态环境数学模型当系统存在正平衡态时,通过利用Hale-Waltman关于一致持久的定理,得到了系统的一致持久性.也证明了当caμ相似文献   

PERSISTENCE OF NONAUTONOMOUS PREDATOR-PREY SYSTEMS WITH INFINITE DELAY

Nonautonomous predator-prey systems with infinite delay is considered at phase space Cg in this paper. Some suitable conditions of persistence of the populations are obtained. The results are different from ones of Wang Ke which was considered in phase space Ch     

THE HETEROCLINIC CYCLE IN THEMODEL OF COMPETITION BETWEENn SPECIES AND ITS STABILITY

1.IntroductionConsidertheanalogousGause-Lotka-Volterra(GLV)differentialequationsforncompetingpopulationsMayandLeonard[ll,Hcf'bauerandSigmundl21havestudiedthissystemforthecasen=3separately.Bothofthemnotedthatinsuchsystemprobablythereexistsaheterocliniccycle.Biologically,thestudyoftheheterocliniccycleisinterestingsinceitsstabilityiscloselyrelatedtothepermanenceproblem.Ontheotherhand,inrecelltyearsmathematicianshavestudiedwithinterestthestabilityofaheterocltalccycleandthebifurcationofit.Inth…     

PERSISTENCE AND PERIODIC SOLUTIONS FOR NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH IMPULSES

In this paper, a nonautonomous Predator-prey model with functional response and impulses is studied. By using comparison theorem and the mono-tonicity, some sufficient conditions which guarantee the permanence and asymptotic behavior of this system are obtained.     

一类离散生态经济系统稳定性与分支研究

本文研究了一个离散生态经济模型的稳定性和分支问题.利用离散奇异系统理论,中心流形定理及Neimark-Sacker分支理论,得到了系统关于不动点的稳定性和Neimark-Sacker分支的有关结果,并与相应的连续模型进行对比分析.推广了文献[5]的结果.     

一类带有扩散和时滞的捕食与被捕食模型的渐近性质

本文中，我们考虑一类带有扩散和时滞的捕食与被捕食系统．我们分析了系统的非负不变性，边界平衡点性质，全局渐近稳定性及永久持续生存性．在这一系统中，当时滞由0变到ro时，系统在平衡点附近发生Hopf分支．即当r增加通过临界值ro时，从正平衡点分支出周期解．     

ALMOST PERIODIC SOLUTION OF A NONAUTONOMOUS MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH NONMONOTONIC FUNCTIONAL RESPONSE AND A PREY REFUGE

A nonautonomous modified Leslie-Gower predator-prey model with nonmonotonic functional response and a prey refuge is proposed and studied in this paper. Sufficient conditions which guarantee the permanence, extinction of the prey species and the global stability of the system are obtained, respectively. Also, by constructing a suitable Lyapunov function, some sufficient conditions are obtained for the existence of a unique globally attractive positive almost periodic solution of this model. Our results indicate that the prey refuge has positive effect on the coexistence of the species. Examples together with their numeric simulation show the feasibility of our main results.     

灰色时变离散系统的稳定性分析

本文讨论了一类灰色时变离散系统和一类具有时滞的灰色时变离散系统的稳定性问题．利用比较原理和差分不等式获得了一些简单的代数判据