含连续时滞的二维竞争系统的周期解和循环解

本文利用HOPf分支定理和Birkhoff定理给出了含连续时滞的二维Lotka-Volterra竞争系统存在周期解和循环解的条件。     

具有无穷时滞的一个捕食者-两个竞争被捕食者生态动力学模型的动力学研究（英文）

提出了一类具有时滞的一个捕食者一两个竞争被捕食者生态动力学模型.首先,利用Krasnoselskii不动点定理研究了系统的正周期解的存在性;然后通过构造Lyapunov函数方法获得了正周期解全局收敛的一个充分条件:最后.给出一个例子以验证理论结果的正确性.     

一类具有无穷时滞的不连续Lasota-Wazewska模型及其伪概周期性

本文研究了一类具有无穷时滞的不连续Lasota-Wazewska模型及其伪概周期性.首先利用指数二分性和不动点定理证明该系统伪概周期解的存在唯一性,然后通过构造恰当的Lyapunov函数得到伪概周期解的指数收敛性.最后,给出一个实例验证本文结论的可行性.     

一个造血模型的概周期正解的存在唯一性和全局吸引性

本文讨论了一类具有无穷时滞的泛函微分方程 N′（t）=-α（t）N（t）＋b（t）∫0^∞K（s）e^-q（t）N（t-s）ds,t≥0, 正概周期解的存在唯一性和全局吸引性问题,利用锥中不动点定理,不仅得到了上述系统的正概周期解的存在唯一性和全局吸引性的结论,还改进了文献[15]的主要结果,并且我们的方法比压缩映象原理要好．如果（＊）中所有的系数都为周期的,相应的结论也是成立的,此时,我们的结果也推广了现有文献的结论．     

具年龄结构和时滞的自食种群系统的周期解

利用延拓定理讨论具年龄结构和时滞的自食种群系统正周期解的存在性,得到周期解存在的条件,推广了已有结论.     

具性别结构时滞捕食系统的Hopf分支,混沌与脉冲控制

建立了具性别结构的时滞捕食系统,研究了平衡点的存在性及局部稳定性,给出了系统发生局部Hopf分支的充分条件,并应用中心流形定理研究了Hopf分支周期解的性质(分支类型,方向及稳定性).数值例子佐证了理论结果,并揭示了系统诸如高倍周期及拟周期振荡,混沌振荡,倍周期分岔等复杂的动力学行为;脉冲控制可以有效的改善系统的稳定性.     

具脉冲出生的Leslie-Gower捕食者-食饵系统的动力学分析

研究了一个具有脉冲出生的Leslie-Gower捕食者一食饵系统的动力学性质．利用频闪映射。得到了带有Ricker和Beverton-Holt函数的脉冲系统准确的周期解．通过Floquet定理和脉冲比较定理,讨论了该系统的灭绝和持久生存．最后,数值分析了以b（p）为分支参数的分支图,得到的结论是脉冲出生会带给系统倍周期分支、混沌以及在混沌带中出现周期窗口等复杂的动力学行为．     

Gause比率依赖型捕食者-食饵系统的周期解

考虑一类Gause比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理, 研究了全局周期解的存在性,得到保证周期解存在的充分条件．     

时标上具有HollingⅢ型功能反应的捕食模型的周期解

研究了时标上一类具有Holling型功能反应的捕食模型.运用时标上连续拓扑度定理,得到了系统存在周期解的充分条件,从而使系统的连续时间情形和离散时间情形的周期解问题得到了统一,该方法可广泛应用于研究微分方程和差分方程的周期解的存在问题.     

一类基于比例确定的离散Leslie系统正周期解的存在性

利用重合度理论中的延拓定理讨论了一类具Holling-Tarmer Ⅱ类功能反应比例确定的离散周期Leslie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。     

具有阶段结构和群体防卫的脉冲捕食系统

讨论了食饵具有群体防卫和捕食者具有阶段结构的脉冲控制捕食系统,根据Floquet乘子理论和脉冲比较定理,获得了食饵（害虫）灭绝周期解局部稳定与系统持续生存的充分条件．利用Matlab软件对害虫灭绝周期解和害虫周期爆发现象进行了数值模拟,并揭示了诸如高倍周期振荡,混沌,吸引子突变等复杂的动力学现象．得出的结论为害虫治理提供了可靠的策略依据．     

The geometrical analysis of a predator-prey model with two state impulses

Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results.     

多滞量捕食模型的正周期解

利用重合度理论中的延拓定理讨论了多滞量捕食模型的正周期解的存在性,得到了保证周期解存在的充分条件,推广了已知的相关结果。     

具有阶段结构的两种群竞争系统的周期解

本文研究了具有阶段结构的两种群竞争系统的渐近行为.我们得到了系统持续生存的条件.由Brouwer不动点定理和李亚普诺夫函数,我们证明相应的周期系统在满足一定的条件下,存在一个唯一的全局渐近稳定的正周期解.最后我们把没有阶段结构的系统与有阶段结构的系统进行了比较.     

An impulsive delayed SEIRS epidemic model with saturation incidence

A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using Krasnoselskii's fixed-point theorem, we obtain the existence of infection-free periodic solution of the impulsive delayed epidemic system. We define some new threshold values R(1), R(2) and R(3). Further, using the comparison theorem, we obtain the explicit formulae of R(1) and R(2). Under the condition R(1) < 1, the infection-free periodic solution is globally attractive, and that R(2) > 1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ* and the disease is uniformly persistent if the vaccination rate is less than θ(*). Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Moreover, we prove that the disease will be permanent as R(3) > 1.     

具有脉冲效应和一般功能性反应的一类时滞捕食者-食饵系统的周期解(英文)

利用重合度理论中的延拓定理,得到了具有脉冲效应和一般功能性反应的一类时滞捕食者-食饵系统的正周期解存在的充分条件.     

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.