生态扩散系统全局渐近稳定的条件

本文研究一类带扩散的非自治捕食系统,该系统由ｎ个斑块组成,食饵种群可以在ｎ个斑块之间扩散,而捕食者种群限定在一个斑块不能扩散．得到系统持续生存和全局渐近稳定的条件．     

具有扩散的n斑块生态系统的渐近周期解

研究了具有渐近周期系数的两种群扩散竞争系统,该系统由n个斑块组成,其中一种群可以在n个斑块之间扩散,而另一种群在一个斑块中,不能扩散.结合运用Liapunov函数,得到该系统唯一存在全局渐近稳定的渐近周期解的条件.     

捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.     

脆弱斑块中植物种子的脉冲扩散

考虑了一类脆弱斑块中植物种子的脉冲漂移模型,得到了系统永久持续生存性.在此基础上,利用单调凸算子理论,得到了系统唯一全局渐进稳定的周期解.数值模拟也表明脉冲扩散能挽救脆弱斑块中的植物种群.     

具有功能性反应和时滞的扩散捕食-食饵系统

考虑具有功能性反应和时滞的扩散捕食-食饵系统，其中食饵连两个斑块间具有一定的扩散系数，捕食者可以两个斑块中任意走动，我们讨论了系统的一致持久性和周期解的存在性及全局吸引性．     

N-种群Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性

本文研究了一类具有ai类功能性反应函数的n种群非自治Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性．利用比较原理和构造Lyapunov函数分别得到系统的持久生存与全局渐近稳定的充分条件．     

基于污染环境毒素驱使下扩散的随机单种群系统的生存分析

研究了一类基于污染斑块环境毒素驱使下扩散的单种群模型.通过构造合适的Lyapunov函数分析了系统存在唯一的全局正解,并讨论了解的随机最终有界性;最后获得了种群随机持久、均值持久和灭绝的充分条件.     

具有避难所的非自治竞争系统的持续生存和全局稳定性

考虑一个四缀块模型，其中一缀块里有三个竞争种群，另外三个分别是它们的避难所，并且种群能在竞争缀块和各自的避难所间相互扩散．在一定的条件下，我们给出了此模型的持续生存，周期性和全局稳定性．     

三个种群的反应-扩散-趋化项系统的耗散结构和模式形成

三个种群的反应-扩散-趋化项系统的耗散结构和模式形成是由其中两个种群的捕食者竞争一种食铒而发展的.文章分别研究了随机扩散系统和定向扩散系统.并提供了一些数值模拟来支持我们的结果.     

非局部时滞Schoner竞争反应扩散方程的行波解

构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型．每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的．我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性．     

PERMANENCE OF A NONLINEAR PERIODIC PREDATOR-PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENCE

In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.     

PERSISTENCE AND PERIODIC ORBITS FOR TWO-SPECIES NON-AUTONOMOUS DIFFUSION LOTKA-VOLTERRA MODELS

A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time dependent. It is shown that the system can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.     

Permanence and extinction analysis for a delayed periodic predator-prey system with Holling type II response function and diffusion

In this paper, it is studied that two species predator-prey Lotka-Volterra type dispersal system with delay and Holling type II response function, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions of integrable form for the boundedness, permanence, extinction and the existence of positive periodic solution are established, respectively.     

具有连续时滞和比率型功能反应的竞争系统的正周期解的存在性

本文利用重合度理论中的延拓定理讨论了具有连续时滞和比率型功能反应的非自治扩散竞争系统的正周期解的存在性,得到了正周期解存在的充分条件。     

Persistence and periodic orbits for two-species nonautonomous diffusion lotka-volterra models

This paper considers a competing system in which one of two species can diffuse between two patches, while the other is confined to one patch and cannot diffuse. It is proved that the system can be made persistent under some appropriate conditions even if the competitive patch is not persistent without diffusion. Further, if the system is a periodic system, it can have a strictly positive periodic orbit which is globally asymptotically stable under the appropriate conditions.     

On a nonlinear nonautonomous predator–prey model with diffusion and distributed delay

In this paper, a nonlinear nonautonomous predator–prey model with diffusion and continuous distributed delay is studied, where all the parameters are time-dependent. The system, which is composed of two patches, has two species: the prey can diffuse between two patches, but the predator is confined to one patch. We first discuss the uniform persistence and global asymptotic stability of the model; after that, by constructing a suitable Lyapunov functional, some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained. An example shows the feasibility of our main results.     

Existence and global stability of positive periodic solutions for predator–prey system with infinite delay and diffusion

In this paper, we study a periodic predator–prey system with Holling type III functional response, in which the prey species can diffuse among two patches but the predator is confined in one patch. By using the continuation theorem of coincidence degree theory and Lyapunov functional, some sufficient conditions are obtained.     

Permanence for a class of periodic time-dependent predator–prey system with dispersal in a patchy-environment

In this paper, we study two species predator–prey Lotka–Volterra type dispersal system with periodic coefficients in two patches, in which both the prey and predator species can disperse between two patches. By utilizing analytic method, sufficient and realistic conditions on permanence and the existence of periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.     

Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent

In this paper, we study two species time-delayed predator-prey Lotka-Volterra type dispersal systems with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this systems are established. The theoretical results are confirmed by a special example and numerical simulations.     

PROPERLIES OF ALMOST PERIODIC SOLUTION FOR A KIND OF ECOLOGICAL SYSTEMSWITH TIME DELAY

AMSSubjectClassification34C27Thespatialelementinpopulationbiologyisimportanttounderstandthedynamicsofecologicalsystems.ThetheoreticalworksonthisproblemwerepioneeredbySkellamif]in1951andwerereviewedbyLevin[2]in1974.In12],Levinfirstestablishedthiskindofmode…