具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

周期二维Lotka—Volterra系统的一些新结果

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．     

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．     

Holling IV捕食-食饵时滞系统的多个周期解

应用重合度定理研究了一类具有Holling IV类功能性反应时滞捕食-食饵系统的周期解的存在性问题,建立了该系统具有至少两个正周期解的充分条件．     

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

讨论了与害虫治理相关的一类捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界．得出的结论为现实的害虫治理提供了可靠的策略依据．     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

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．     

捕食者一食Lotka—Volterra系统的概周期解

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．     

带有扩散、脉冲和时滞的非自治捕食系统的正周期解

考虑了一类食饵在斑块环境中扩散具有脉冲和时滞的捕食系统，通过灵活地运用Gaines和Mawhin的连续拓扑度定理，获得了一系列易验证的正周期解存在的充分条件．     

扩散Beddington-DeAngelis捕食食饵模型的行波解

主要研究捕食者和食饵皆具有一般密度制约的扩散Beddington-DeAngelis捕食-食饵模型的行波解.通过构造行波系统的Wazewski集和Lyaponov函数,应用拓扑打靶法的方法建立系统连结边界平衡点到共存平衡点的轨道,进而证明原扩散系统连结边界平衡点到共存平衡点的非负行波解的存在性.     

时滞速度反馈对强迫自持系统动力学行为的影响

研究强迫自持振动系统因时滞反馈产生的主共振解及其分岔．通过对强迫非自治系统的时滞反馈控制,得到所要研究的数学模型．讨论对应的线性化系统使平凡平衡态失稳出现周期解的稳定性临界条件．特别关注主共振及分岔．结果表明,稳定的主共振解随着时滞的变化周期性地出现在系统中．同时,也给出了不稳定的主共振关于时滞变化的区域,在理论方面给出了系统出现概周期运动的时滞区域．数据模拟证实了理论结果．     

Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with periodically varying substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Furthermore, we numerically simulate a model with sinusoidal input, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the periodic system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat

In this paper, we introduce and study a model of a predator–prey system with Monod type functional response under periodic pulsed chemostat conditions, which contains with predator, prey, and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout

In this paper, we introduce and study a model of a Monod type food chain chemostat with pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halving.     

Analysis of competitive chemostat models with the Beddington–DeAngelis functional response and impulsive effect

In this paper, we introduce and study a competitive system with Beddington–DeAngelis type functional response in periodic pulsed chemostat conditions. We investigate the subsystem with substrate and one of the microorganisms and study the stability of the periodic solutions, which are the boundary periodic solution of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate and one of the microorganism. Further, we prove that the system is permanent if the impulsive period less than some critical value. Therefore, our results are valuable for the manufacture of products by genetically altered organisms.     

具有密度依赖的生育脉冲单种群阶段结构模型

给出具有密度依赖生育脉冲单种群阶段结构数学模型．通过研究其频闪映射所确定的离散动力系统,获得了具有生育脉冲的系统存在周期解及其稳定的阈值,当系统的参数超过阈值,存在一系列的分支并最终走向混沌,这说明生育脉冲使系统动力学行为变得非常复杂,提供了一个自然的周期,而使系统从倍周期分支到混沌．     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。     

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.     

水发汗冷却控制模型解的稳定性

本文研究了带活动边界的水发汗控制系统解对初边值条件及控制参数的连续依赖性 ,稳定性 .     

Boundedness and Almost Periodicity of Solutions for a Class of Semilinear Parabolic Equations with Boundary Degeneracy

In this paper the authors investigate the boundedness and almost periodicity of solutions of semilinear parabolic equations with boundary degeneracy. The equations may be weakly degenerate or strongly degenerate on the lateral boundary. The authors prove the existence, uniqueness and global exponential stability of bounded entire solutions, and also establish the existence theorem of almost periodic solutions if the data are almost periodic.