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1.
In this paper, we deal with a discrete predator-prey system with delay. We first give a sufficient condition for the uniform persistence of the system. Assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa's theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays, we obtain the existence of a periodic solution basing on the uniform persistence result.  相似文献   

2.
Given an autonomous system with an isolated equilibrium, we consider general periodic perturbations. We say that the equilibrium persists if it can be continued as a periodic solution. The question of persistence is very classical and we find that the search of sharp conditions is linked with Topology. Besides the topological degree, the notion of diffeotopy and Hopf?s Theorem of homotopy classes play a role. For dimension two we find a complete characterization of persistence.  相似文献   

3.
一类概周期时滞捕食-食饵系统的概周期解   总被引:3,自引:0,他引:3  
本文讨论一类概周期时滞捕食-食饵系统的一致持久性,通过构造一个Liapunov函数得到该系统有界解的唯一性,并且给出正概周期解的存在唯一性定理。  相似文献   

4.
The uniform persistence is proved for a non-autonomous competitive and prey-predator model with ratio-dependent functional response and stage-structure. By constructing a Liapunov functional, we establish the conditions of existence and uniqueness for the positive periodic solution, which is globally asymptotically stable. We get a unique almost periodic solution for an almost periodic system as well under corresponding conditions .by means of the Razumikhin function method.  相似文献   

5.
In this paper, we investigate an HIV model incorporating the effect of an ARV regimen. Since drug concentration varies during dose intervals, which results in periodic variation of the drug efficacy, our model is then a periodic time-dependent system. We get a threshold value between the extinction and the uniform persistence of the disease by applying the persistence theory. Our main results show that the disease goes to extinction if the threshold value is less than unity, whilst the disease persists if the threshold value is larger than unity. We also prove that there exists a positive periodic solution which is globally asymptotically stable. The threshold dynamics is in agreement with that for the system with constant coefficients, which extends the classic results for the corresponding autonomous model.  相似文献   

6.
This paper discusses a discrete Lotka-Volterra competition system. We first obtain the persistence of the system. Assuming that the coefficients in the system are periodic, we obtain the existence of a periodic solution. Moreover, under some additional conditions, this periodic solution is globally stable. Our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature.  相似文献   

7.
In this paper we give the sufficient and necessary conditions of the uniform persistence for periodic predator-prey Lotka- Volterra systems. That is, the system is uniformly persistent if and only if any one of the semi-trivial periodic solutions is linearly unstable.  相似文献   

8.
In this paper, we consider a time-delayed periodic system which describes the competition among mature populations. By appealing to theories of monotone dynamical systems, periodic semiflows and uniform persistence, we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion.  相似文献   

9.
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain in [15] on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract “counter-term theorem” à la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find “many more” almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.  相似文献   

10.
该文研究周期二维Lotka-Volterra捕食食饵系统解的有界性,持续生存性以及正周期解的存在性和全局稳定性.并将结果推广到食饵有补充的周期二维Lotka-Volterra竞争系统上去,得到了一系列新的结果,改进和推广了文[1—3]的主要结论.  相似文献   

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