不动点理论与里卡提方程两个正周期解的存在性

利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.     

Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion

By employing the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established. Further, by constructing a Lyapunov functional and using the result of the existence of positive periodic solution, the attractivity of a positive periodic solution for above system is obtained.     

Logistic型方程周期解和概周期解的存在性

In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.     

Uniqueness and exponential stability of almost periodic positive solution for Lasota‐Wazewska model with impulse and infinite delay

In this paper, impulsive Lasota‐Wazewska model with infinite delay is studied. By using fixed point theorem of decreasing operator, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence, which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by Liapunov functional. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic behavior of an eco-epidemic system with impulsive birth

In the paper, we investigate an eco-epidemic system with impulsive birth. The conditions for the stability of infection-free periodic solution are given by applying Floquet theory of linear periodic impulsive equation. And we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes. By using the method of coincidence degree, a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.     

Globally asymptotical stability and periodicity for a nonautonomous two-species system with diffusion and impulses

Existence and globally asymptotical stability of positive periodic solutions for a nonautonomous two-species competition system with diffusion and impulses are studied in this paper. By employing Mawhin continuation theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one positive periodic solution, and by means of a suitable Lyapunov functional, the globally asymptotical stability of positive periodic solution is presented. Finally, an illustrative example and simulations are given to show the effectiveness of the main results.     

Dynamical behaviors of a prey-predator system with impulsive control

In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis.     

具有扩散和时滞的捕食系统的持续生存

本文研究具有一般功能性反应和时滞的周期捕食系统的持续生存和周期解,得到了系统永久持续生存的充要条件.在此条件下系统存在正的ω周期解,改进了一些已知结果.     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

具有三个年龄阶段的自食单种群时滞模型的周期解

利用重合度理论中的延拓定理讨论了一个具有三个成长阶段的自食单种群时滞模型正周期解的存在性,得到了保证周期解存在的充分条件.