非自治多种群时滞Kolmogorov系统的持续性和灭绝性

研究非自治多种群时滞Kolmogorov系统,给出了该系统中种群持续和灭绝的充分条件,并把得到的结果应用于非自治时滞Lotka-Volterra系统.把相关文献的有关结果推广到时滞系统.     

具有时滞的非自治Lotka-Volterra竞争系统的持久与灭绝

本文研究具有纯时滞的一般Ｎ－种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的持久性和灭绝性．一些新的判别准则被建立．文献［８－１０］中得到的关于无时滞非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的结果被改进和推广．     

具有时滞的非自治Lotka-Volterra竞争系统的持久与灭绝

本文研究具有纯时滞的一般Ｎ－种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的持久性和灭绝性．一些新的判别准则被建立．文献［８－１０］中得到的关于无时滞非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的结果被改进和推广．     

Nonautonomous Lotka-Volterra Systems with Delays

The paper studies the general nonautonomous Lotka-Volterra multispecies systems with finite delays. The ultimate boundedness, permanence, global attractivity, and existence and uniqueness of strictly positive solutions, positive periodic solutions, and almost periodic solutions are obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra multispecies systems without delay to systems with delay.     

The criteria of ultimate boundedness for nonautonomous Lotka-Volterra tree systems

In this paper, by introducing a concept called the degree of species, we obtain a set of sufficient conditions for the ultimate boundedness of nonautonomous n-species Lotka-Volterra tree systems. As a consequence, we also obtain the criteria of the existence of a globally stable equilibrium point for the autonomous Lotka-Volterra tree system. The criteria in this paper are in explicit forms of the parameters, and thus, are easily verifiable.     

具有时滞的一类N-种群非自治竞争系统的持久性(英文)

讨论了具有时滞的一类N-种群非自治竞争系统.建立了系统持久的新条件.推广了文献[1]中的结果.     

一类非纯时滞非自治Lotka-Volterra竞争系统的持久性

讨论一类非纯时滞非自治Lotka-Volterra竞争系统,通过改进[4],[5]和[6]中一些方法,得到所有种群持久的充分条件,其结果推广了[4]的结论.     

THE EXTINCTION IN NONAUTONOMOUS PREY-PREDATORLOTKA-VOLTERRA SYSTEMS

1.IntroductionConsiderthenonautonomousprey-predatorLotka-Volterrasystem:whereal30andxZ20;hi(t)andail(t)(i,j=1,2)arecontinuousandboundedfunctionsdefinedon[0,co).Weassumetbxoughoutthispapera'j(t)20forallt20andi,j~1,2andthatthereealstpositiveconstantsfisuchthatTheextinctionofperiodicpredator-preyLotka-Volterrasystemhasbeenstudiedin[l].Inthispaper,ourpurposeistostudytheextinctionofgeneralnonautonomouspredatorpreyLotka-Volterrasystems.Weshallestablishsomesufficientconditionsandnecessary.Thisres…     

非自治竞争Lotka—Volterra系统的持续生存和全局稳定

本文研究一般ｎ个种群竞争的非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ系统,得到了系统一致持续生存和全局渐近稳定的新的判别准则,这些准则推广了现有有关文献中的一些结果。     

Global stability for separable nonlinear delay differential systems

In this paper, we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution. Applying these, we offer improved 3/2-type criteria for global asymptotic stability of nonautonomous Lotka-Volterra systems with delays.     

Permanence and global stability for nonautonomous N-species Lotka-Volterra competitive system with impulses and infinite delays

In this paper, we consider a class of nonautonomous N-species Lotka-Volterra competitive systems with impulses and infinite delays. By developing the methods given in Teng (2002) [25], we give sufficient conditions for permanence and global attractivity of the system.     

POSITIVE ALMOST PERIODIC SOLUTIONS OF n DIMENSIONAL NONAUTONOMOUS LOTKA-VOLTERRA COMPETITIVE SYSTEMS

In this paper,we study some n dimensional nonautonomous Lotka-Volterra competitive ecological systems.We then obtain permanence of such systems, as well as the existence,uniqueness and global asymptotic stability of almost periodic positive solutions to these systems.     

On blow-up solutions for systems of semilinear heat equations with quadratic nonlinearities

This article deals with blow-up solutions of the Cauchy–Dirichlet problem for system of semilinear heat equations with quadratic non-linearities. Sufficient conditions for the existence of blow-up solutions are established. Sets of initial values for these solutions as well as upper bounds for corresponding blow-up time are determined. Furthermore, an application to the Lotka-Volterra system with diffusion is also discussed. The result of this article may be considered as a continuation and a generalization of the results obtained in (Baris, J., Baris, P. and Ruchlewicz, B., 2006, On blow-up solutions of nonautonomous quadratic differential systems. Differential Equations, 42, 320–326; Baris, J., Baris, P. and Wawiórko, E., 2006, Asymptotic behaviour of solutions of Lotka-Volterra systems. Nonlinear Analysis: Real World Applications, 7, 610–618; Baris, J., Baris, P. and Ruchlewicz, B., 2006, On blow-up solutions of quadratic systems of differential equations. Sovremennaya Matematika. Fundamentalnye Napravleniya, 15, 29–35 (in Russian); Baris, J. and Wawiórko, E., On blow-up solutions of polynomial Kolmogorov systems. Nonlinear Analysis: Real World Applications, to appear).     

非自治Lotka-Volterra竞争生态系统的绝灭性和持久性

研究一般n个竞争种群的非自治Lotka-Volterra生态系统．得到了该系统一致持续生存和绝灭性的新的判别准则，这些结果改进和推广了文献[1，2]中的主要结果．     

Permanence and global attractivity for discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls

A discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls is proposed and investigated. By using the method of discrete Lyapunov functionals, new sufficient conditions on the permanence of species and global attractivity of the system are established. Particularly, an interesting fact is found in our results, that is, the feedback controls are harmless to the permanence of species for the considered system.     

Extinction in nonautonomous competitive Lotka-Volterra systems

It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the species nonautonomous competitive Lotka-Volterra model, we exhibit simple algebraic criteria on the parameters which guarantee that all but one of the species is driven to extinction. The restriction of the system to the remaining axis is a nonautonomous logistic equation, which has a unique solution that is strictly positive and bounded for all time; see Coleman (Math. Biosci. 45 (1979), 159-173) and Ahmad (Proc. Amer. Math. Soc. 117 (1993), 199-205). We prove in addition that all solutions of the -dimensional system with strictly positive initial conditions are asymptotic to .

     

一类滞后型非自治的捕食者-食饵系统的周期解

本文研究了一类滞后型三种群捕食者-食饵Lotka-Volterra系统.利用重合度理论 建立了这类系统正周期解的存在性判据.     

一类Lotka-Volterra互惠扩散系统的概周期解和全局稳定性

In this paper a nonautonomous two-species n-patches system is studied.Within each patch,there are two cooperative species and their dynamics are described by the LotkaVolterra model.Each species can diffuse independently and discretely between its interpatch and intrapatch.By constructing a suitable Liapunov function,some sufficient conditions are obtained for the existence of a unique globally asymptotically stable positive almost periodic solution.     

一类Lotka-Volterra捕食-竞争扩散系统的概周期解

研究了一类带扩散项的n种群Lotka-volterra非自治捕食-竞争系统，应用Liapunov泛函方法得到系统持久生存和存在唯一全局渐近稳定正概周期解的新的充分条件，并举例说明定理的应用．     

Extinction in nonautonomous competitive Lotka-Volterra systems with infinite delay

The principle of competitive exclusion is extended to n-species nonautonomous Lotka-Volterra competition systems of differential equations with infinite delay. It is shown that if the coefficients are bounded, continuous and satisfy certain inequalities, then any solution with initial function in an appropriate space will have n−1 of its components tend to zero, while the remaining one will stabilize at a certain solution of a logistic differential equation.