具有时滞和反馈控制的离散Leslie系统的概周期解

讨论了具有时滞和反馈控制的离散Leslie概周期捕食与被捕食系统.利用差分不等式和通过构造适当的Lyapunov函数,得到了系统持久性和全局吸引的充分条件.利用泛函概周期的壳理论,得到了系统存在唯一全局吸引概周期解的充分条件.     

具有扩散率Ayala模型的概周期解

本文研究了非自治Ayala模型的概周期和周期系统,我们得到在一定条件下,其概周期系统存在唯一全局吸引的概周期解且其概周期解在壳扰动下是稳定的。在与概周期情形类似的条件下我们得到其w-周期系统存在唯一全局吸引的w-周期解。     

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.     

具有粘弹性和热粘弹性方程组的全局周期吸引子

证明了具有粘弹性和热粘弹性方程组在Dirichlet边界条件下,对于任意的非自治时间周期受迫力,均具有唯一的指数吸引任何有界集的周期解,即全局周期吸引子.并且如果受迫力是自治的,则全局周期吸引子恰是系统唯一的指数吸引有界集的平衡解.     

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.     

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.     

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.     

一类单种群系统正周期解及其稳定性

考虑周期单种群模型 dxdt=xg( t,x)± p( t,x)的正周解及其稳定性 .证明了在一定条件下 ,系统存在全局吸引的正周期解 .给出了系统存在两个正周期解的充分条件 ,同时也给出了种群灭绝的条件 .这些结果用于 Logistic模型和 Odum模型 ,得到了被开发的周期 Logistic模型存在全局吸引的正周期解 ;被开发了的周期 Odum模型只存在两个正周期解 ,其中之一吸引初值大于一个定数的所有解 ,另一个周期解则是种群灭绝的分界线     

具脉冲扰动的时滞Ivlev型捕食系统

构建了具脉冲扰动的时滞Ivlev型捕食系统,获得了捕食者灭绝周期解全局渐近吸引和系统持续生存的充分条件.数值例子验证了理论结果,揭示了系统诸如吸引子突变,高倍周期振动,分支等复杂的动力学行为,最后进行了总结与讨论.     

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.     

On small perturbations of a nonlinear periodic system with degenerate equilibrium

This paper considers the reducibility and existence of periodic solutions for a class of nonlinear periodic system with a degenerate equilibrium point under small perturbations. By introducing some parameter, we consider an equivalent periodic system. Then we prove that by an affine linear periodic transformation the parameterized periodic system is reducible to one with zero as an equilibrium. Topological degree theorem ensures that for some parameter the result can go back to the original system. Then, we obtain a small periodic solution.     

On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay

A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained.     

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.     

Some new results for a logistic almost periodic system with infinite delay and discrete delay

A nonautonomous logistic almost periodic system with infinite delay and discrete delay is considered. Our result shows that the system is globally asymptotically stable under the condition for the boundedness of the system. By using almost periodic functional Hull theory and new computational techniques, we show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution under the condition for the boundedness of the system. Some recent results are improved, and an open question is answered.     

A periodic predator–prey-chain system with impulsive perturbation

A periodic predator–prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied.     

Periodic solution and almost periodic solution for a nonautonomous Lotka-Volterra dispersal system with infinite delay

This paper studies a nonautonomous Lotka-Volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal. Our results show that the system is uniformly persistent under an appropriate condition. The sufficient condition for the global asymptotical stability of the system is also given. By using Mawhin continuation theorem of coincidence degree, we prove that the periodic system has at least one positive periodic solution, further, obtain the uniqueness and globally asymptotical stability for periodic system. By using functional hull theory and directly analyzing the right functional of almost periodic system, we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution. We also show that the delays have very important effects on the dynamic behaviors of the system.     

On isolated periodic solutions of differential systems

Summary The concept of an isolated periodic solution of a periodic differential system is defined and it is proved that if the number 1 is not a characteristic multiplier of the variational system corresponding to the given periodic solution then this solution is isolated. The concept of a periodic solution with isolated path of an autonomous system is defined and it is proved that if the number 1 is a simple characteristic multiplier of the corresponding variational system then the periodic solution has an isolated path. An example is given showing that the conditions above are not necessary. Entrata in Redazione l’8 giugno 1974.     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

ASYMPTOTIC BEHAVIOR OF THE POSITIVE SOLUTION OF A NONAUTONOMOUS FOOD-CHAIN MODEL WITH DIFFUSION

A nonautonomous food-chain system with diffusion is investigated in this paper, whose coefficients asymptotically approach periodic functions. Under some sufficient conditions all positive solutions of the system asymptotically approach the periodic solution of the corresponding periodic system, by using comparison theorem and constructing Lyapunov-type functions.