具有反馈控制的离散两种群竞争系统的概周期解

对于具有反馈控制的离散概周期两种群竞争系统的概周期解问题,进行了深入的讨论,得到了该系统存在唯一的一致渐近稳定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。     

一类非线性微分方程的概周期解

运用Leray-Schauder不动点定理和Liapunov函数方法,研究了一类非线性微分方程的概周期解,得到了该微分方程概周期解存在的充分条件.     

捕食者-食Lotka-Volterra系统的概周期解(英文)

研究了有m个捕食者n个食饵的概周期Lotka-Volterra系统.得到了系统共存的条件.此外,还得到了系统概周期解存在唯一并且全局渐近稳定的条件.     

具有反馈控制的N种群非自治LOTKA-VOLTERRA竞争系统的概周期解的存在性

讨论了具有反馈控制的N种群非自治LOTKA-VOLTERRA竞争系统,获得了该系统概周期解的存在性和全局稳定性,改进了概周期解研究的方法.     

一类非线性时滞系统概周期解的存在唯一性

应用Liapunov，泛函，研究了一类时滞系统概周期解的存在唯一性，得到了保证系统存在唯一概周期解的一组充分条件．     

全局渐近稳定性质与概周期解的存在唯一性

众所周知,周期系统解的有界性蕴含着周期解的存在性。然而对于概周期系统(1)来说,即使在n=1的情况下其解的有界性也未必蕴含着概周期解的存在性。因此,在讨论(1)的概周期解的存在性时,必需同时考虑有界解的某种稳定性质。 本文首先证明当研究概周期系统(1)的概周期解φ(t)的稳定性时,可假设φ(t)是明显解。其次,我们利用李雅普诺夫函数和比较原理得到了(1)的零解为全局等度(均匀)渐近稳定的一些结果。最后,我们亦得到了(1)存在唯一概周期解的充分条件。所得结果推广了[1,11,13]中有关结论。     

一类Lotka-Volterra竞争系统概周期解的存在和多解性

利用延拓定理和分析技巧,研究一类带收获项的时滞脉冲Lotka-Volterra竞争系统的概周期解的存在和多解性,得到了概周期解的存在和多解性的充分条件.最后给出一个实例说明结论的可行性.     

时标上具Allee效应的动力学方程的概周期解

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

时标上具Allee效应的动力学方程的概周期解（英文）

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

一类时滞脉冲微分方程的概周期解的存在性

运用锥上的不动点定理，研究一类脉冲时滞微分方程的概周期解，得到了保证系统存在概周期解的一组充分条件。     

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.     

On a theorem of Favard

We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

     

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

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Global dynamics behaviors for a nonautonomous Lotka–Volterra almost periodic dispersal system with delays

A nonautonomous Lotka–Volterra dispersal system with continuous delays and discrete delays is considered. By using a comparison theorem and delay differential equation basic theory, we obtain sufficient conditions for the permanence of the population in every patch. By constructing a suitable Lyapunov functional, we prove that the system is globally asymptotically stable under some appropriate conditions. Using almost periodic functional hull theory, we get sufficient conditions for the existence, uniqueness and globally asymptotical stability for an almost periodic solution. This implies that the population in every patch exhibits stable almost periodic fluctuation. Furthermore, the results show that the permanence and global stability of system, and the existence and uniqueness of a positive almost periodic solution, depend on the delay; then we call it “profitless”.     

时滞微分方程概周期解的存在唯一性

应用Liapunov泛函研究时滞微分方程慨周期解的存在唯一性，去掉了要求预先知道系统存在一个有界解的限制条件．     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.     

一类一阶和二阶微分方程的渐近概周期解

对于一阶微分系统u′+F(u)=h(t),其中F为R~n上的严格单调算子,本文给出了其渐近概周期解存在和唯一的一个充分条件和一个必要条件.特别,对于一阶微分系统u′+▽Φ(u)=h(t),其中▽Φ代表R~N上凸函数Φ的梯度,讨论了其渐近概周期解存在和唯一的充分必要条件,并且把一些结果推广到了一类二阶方程.     

概周期解的存在性、唯一性与稳定性

本文给出了一些保证微分方程的周期解和概周期解的存在性、唯一性、稳定性与不稳定性的充分性条件及周期解的存在范围估计式.所得结果推广[1]的主要结果及[2-6]的有关结果.     

Permanence and almost periodic solution of a Lotka–Volterra model with mutual interference and time delays

In this paper, a Volterra model with mutual interference and time delays is investigated. By applying the comparison theorem of the differential equations and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Two suitable examples together with their numeric simulations are given to illustrate our results by using MatLab.