一类多时滞微分系统的周期解

本文研究了一类多时滞微分系统的周期解的存在性和全局渐近稳定性.利用度理论和一些分析技巧,得到了周期解存在和全局渐近稳定的一个充分条件.推广了文献[8,9,13]的相关结果.     

一类泛函微分方程的周期解的存在性、唯一性及全局吸引性

该文研究了一类具有分布滞量的微分系统的周期解的存在性、唯一性及全局吸引性等问题.利用不动点方法和Lyapunov泛函方法,建立了保证该类系统周期解的存在性、唯一性、一致稳定性及全局吸引性的充分条件.     

一类无穷时滞微分系统的周期解和全局渐近稳定性

利用重合度理论中的延拓定理和微分不等式讨论一类无穷时滞微分系统的周期解的存在性和全局渐近稳定性,获得了简便的判别条件.     

一类具分布时滞的退化微分系统的周期解

本文利用重合度理论讨论一类具分布时滞的退化微分系统的周期解存在性,给出了周期解的存在条件.     

具有离散时滞和反馈控制的Lotka-Volterra合作系统的动力学行为研究

研究了具有离散时滞和反馈控制的两种群Lotka-Volterra合作系统的正周期解的存在性和全局吸引性.基于Gaines和Mawhin的叠合度定理和构造Lyapunov函数的方法,给出了具有离散时滞和反馈控制的两种群周期合作系统的正周期解的存在性和全局吸引性的充分条件.     

含时滞的非自治单种群扩散模型的概周期解的存在性与全局吸引性

研究了含离散时滞的非自治单种群扩散模型的概周期解的存在性与全局吸引性.通过应用微分方程比较原理和不等式估计方法以及构造适当的Lyapunov函数的方法得到了系统的持久性,概周期解存在唯一性,渐进稳定性以及全局吸引性的充分条件.     

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.     

具无穷时滞中立型高维非线性系统的周期解

通过构造算子利用Krasnoselskii不动点定理和线性系统的指数二分性讨论了一类具有无穷时滞非线性中立型高维周期微分系统的周期解存在性问题．得到保证系统存在周期解的新的充分条件．     

一类时滞微分方程非常数周期解的存在性及其个数估计

应用变分方法与无穷维空间Morse理论研究方程=g(x(t-r)),得到上述微分差分方程以4r为周期的非常数周期解存在性的条件,并且给出其个数的下界.因此为研究含有时滞的微分系统周期解的存在性提供了一种新方法.     

具有全局交互作用的时滞周期格微分系统的front-like整体解

研究了一类一维空间周期格上的具有时滞和全局交互作用的微分系统的front⁃like整体解.通过建立适当的比较原理,并融合不同方向的波前解与连接稳定态和不稳定态的空间周期解,构造了front⁃like整体解并证明了一些定性性质.与波前解相比,front⁃like整体解能够展示出新的动力学行为.     

具有分布滞量的微分系统的周期解和全局吸引性

利用重合度理论中的延拓定理和Ｌｙａｐｕｎｏｖ泛函方法讨论一类具有分布滞量的微分系统狓（狋）＝ 犃（狋）狓（狋）＋∫０－狉犳（狋,狊,狓狋＋狊））ｄ狊的周期解的存在性和全局吸引性,得到了便于应用的新结果．     

Global attractivity of the almost periodic solution of a delay logistic population model with impulses

In this paper, we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations. By using a comparison theorem and constructing a suitable Lyapunov functional, a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained. As applications, some special models are studied; our new results improve and generalize former results.     

Existence and global attractivity of positive periodic solutions for impulsive predator–prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator–prey systems with dispersion and time delays. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

Positive periodic solutions for impulsive predator-prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator-prey systems with dispersion and time delays. By using coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of positive periodic solution is presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

Periodic and almost periodic solution for a non-autonomous epidemic predator-prey system with time-delay

In this paper, we studied a non-autonomous predator-prey system with discrete time-delay, where there is epidemic disease in the predator. By using some techniques of the differential inequalities and delay differential inequalities, we proved that the system is permanent under some appropriate conditions. When all the coefficients of the system is periodic, we obtained the existence and global attractivity of the positive periodic solution by Mawhin’s continuation theorem and constructing a suitable Lyapunov functional. Furthermore, when the coefficients of the system are not absolutely periodic but almost periodic, sufficient conditions are also derived for the existence and asymptotic stability of the almost periodic solution.     

一类脉冲时滞宿主一大寄生物系统周期解及全局吸引性(英文)

By using Mawhin continuation theorem,an important lemma and some analysis techniques,sufficient conditions ensuring the existence and global attractivity of positive periodic solutions for an impulsive differential equation with time varying delay are investigated.     

ON THE LASOTA-WAZEWSKA MODEL WITH PIECEWISE CONSTANT ARGUMENT

In this article, a delay differential equation with piecewise constant argument is considered; the existence and global attractivity condition ofalmost periodic solution and quasi-periodic solution are obtained.     

Stability and attractivity of periodic solutions of parabolic systems with time delays

This paper is concerned with the existence, stability, and global attractivity of time-periodic solutions for a class of coupled parabolic equations in a bounded domain. The problem under consideration includes coupled system of parabolic and ordinary differential equations, and time delays may appear in the nonlinear reaction functions. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement using Schauder fixed point theorem, while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme. The results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system. Applications are also given to three Lotka-Volterra reaction diffusion model problems, and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions.     

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.