非自治Lotkz—Volterra扩散模型的持续生存与周期轨道

本文研究了一类非自治的捕食者的一食饵扩散模型；其中食饵能在环境相异的两个缀块间有限制地扩散，但对捕食者来说，缀块间扩散不受任何限制；     

具时滞的非自治的两种群捕食者-食饵缀块系统的持久性

研究了具时滞的非自治的两种群捕食者－食饵缀块系统的持久性，建立了新的判据。     

具有反馈控制和Beddington-DeAngelis功能性反应的非自治扩散模型的概周期解

讨论了一类具有反馈控制和B edd ington-D eA ngelis功能性反应的非自治捕食-食饵扩散模型,其中食饵可以在两个斑块有限制地扩散,但对捕食者来说,斑块间的扩散不受限制.本文结合运用Lyapunov函数,得到该模型存在唯一的全局渐进稳定的正概周期解的条件.     

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．     

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．     

一类三种群捕食者-食饵模型中交错扩散导致的Turing不稳定

本文研究一类具有种内竞争的三种群捕食者-食饵模型的强耦合交错扩散系统,发现当捕食者对食饵的捕获水平高于食饵的种内竞争水平时,捕食者的大的交错扩散系数能够导致Turing不稳定.     

连续收获捕食者与脉冲存放食饵的阶段结构捕食-食饵模型的全局吸引和一致持久

研究了一个捕食者具连续收获与食饵具脉冲存放的阶段结构时滞捕食-食饵模型．根据生物资源管理的实际,改进了捕食者具阶段结构的捕食-食饵模型,即原来假设每个捕食者个体都具有相同的捕食食饵的能力．假设捕食者按年龄分为两个阶段,即幼体和成体,而且幼体无能力捕食食饵．得到了捕食者灭绝周期解全局吸引和系统持久的充分条件．结论说明了脉冲存放食饵对系统的持久起了重要的作用,并且为生物资源管理提供了策略基础．数值分析也进一步说明了系统的动力学性质．     

具有非线性收获的Leslie-Gower捕食者-食饵扩散模型的Hopf分支分析

研究一类具有非线性收获和扩散的Leslie-Gower捕食者-食饵模型.通过对常微分系统和反应扩散系统产生Hopf分支条件的讨论,分析收获和扩散在系统产生Hopf分支中的作用.     

一类捕食者-食饵模型中扩散的作用

本文讨论捕食者带有交错扩散的修正的Leslie-Gower捕食者-食饵模型中各扩散系数的作用.得到的结果表明,交错扩散会导致模型唯一的正常数平衡点失稳.而食饵物种的自扩散则具有抑制失稳发生的作用.     

一类三种群捕食者-食饵交错扩散模型整体解的存在性

应用能量估计方法和Gagliardo-Nirenberg型不等式证明含一类食饵种群和两类竞争捕食者种群的反应扩散模型整体解的存在性和一致有界性,该模型是带自扩散和交错扩散项的三种群捕食者-食饵模型.     

PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

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.     

具有连续时滞和功能性反应的非自治竞争系统的持续生存

本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和Ⅱ类功能性反应的非自治扩散竞争系统．此系统有两个种群n个斑块，其中一个种群可以在n个斑块中自由扩散，另一种群被限定在一斑块中不能扩散．当系数满足一定的条件时，证明了系统是持续生存的，此外，给出了该系统的一周期解全局吸引的充分条件．     

The effect of diffusion on the permanence of Smith population model in a polluted patch

IntroductionThe effect of diffusion on the permanence of population has been studied in some refer-ences. LevinI1] set up the followiIlg model to study the effect of diffusion on the permanence ofpopulation:: f \' \ =.tvhere ur(t) defines the number of population i in patch p, uu = (ut,'. u:). f,u(uu) isthe int!.i11sic growth rate fOr population t, and D:' is the (1iffosive rate of population l frompatch 7 to patch U. Hastingsi2J proved that the positive equilibrium state is stab1e for suf…     

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.     

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

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

DIFFUSION AND BIFURCATION PROBLEMS IN SINGULARLY PERTURBED DOMAINS

ABSTRACT. Diffusion problems under singular perturbations of the domain or the boundary conditions are analyzed. The first problem that we consider is the diffusion of a material from a domain that is nearly impermeable, having only several small patches on the boundary where the material can slowly leak out. The second problem that is studied is the diffusion of a material that originates from some localized regions in a two or three‐dimensional domain. Steady‐state solutions and the long‐time behavior of solutions are analyzed in detail. Finally, the analysis is extended to determine the change in bifurcation values associated with nonlinear diffusion equations under singular perturbations of the domain. The results are then applied to a model in resource management.