一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型的定性分析

考虑了一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型．运用离散动力系统的频闪映射,获得了一个‘微生物灭绝’周期解,进一步获得了该周期解全局吸引的充分条件．运用脉冲时滞泛函微分方程新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是“有害”时滞．     

一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

对一个带有有害时滞与垂直传染的SEIR传染病模型,在脉冲免疫接种条件下,分析了其动力学行为．运用离散动力系统的频闪映射,获得了一个‘无病’周期解,证明了当模型的一些参数在适当的条件下,该‘无病’周期解是全局吸引的．运用脉冲时滞泛函微分方程理论,获得了含有时滞的持久性的充分条件,并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响．结论表明该时滞是“有害”时滞．     

具有增长时滞及脉冲输入的被污染Beddington-DeAngelis恒化器模型的分析

考虑了一类具有增长时滞及脉冲输入的被污染的Beddington-DeAngelis恒化器模型,获得微生物灭绝周期解全局吸引的条件,并运用脉冲时滞微分方程的相关理论、方法和新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是有害时滞.     

在污染环境下竞争Monod恒化器模型的动力学分析

本文考虑了一类在污染环境下具有时滞增长反应及脉冲输入营养基的恒化器模型.获得微生物灭绝周期解全局吸引的充分条件,并运用脉冲微分方程的相关理论和方法,证明了系统在适当的条件下是持久的,结论还表明该时滞是有害时滞.     

具有脉冲和时滞的Logistic模型的持续生存和正周期解的全局吸引性(英文)

本文研究了具有脉冲和时滞效应的Logistic模型.利用脉冲微分方程的比较定理,BohlBrower不动点定理和Lyapunov函数法,获得了系统持续生存,正周期解存在、唯一以及全局吸引的充分条件.结果表明正周期解的全局吸引性与时滞有关.     

在时间尺度上研究带有脉冲的泄漏时滞细胞神经网络反周期解的动态特征

在时间尺度上,通过使用叠合度理论中的连续定理和微分不等式技巧,研究带有脉冲的时变泄漏时滞细胞神经网络模型的反周期解,获得了一些使带有脉冲的时变泄漏时滞细胞神经网络模型的反周期解存在和全局指数稳定的充分条件,并将以前的结论在时间尺度上做了扩展.     

具有Holling Ⅲ功能反应和阶段结构的Gompertz生态系统的持久性

以生态学与微分方程的理论和方法为基础,建立了一类具有HollingⅢ功能反应和阶段结构的生态Gompertz模型.利用频闪映射,获得了捕食者灭绝周期解,分析了此周期解的全局吸引性.在对食饵进行脉冲收获和捕食者具有成长期时滞条件下,运用脉冲微分方程比较定理和小振幅扰动技巧,获得了系统一致持续生存的条件.     

脉冲接种作用下具有时滞的传染病模型分析

本文建立了一类具有潜伏期和免疫期的双时滞SEIRS传染病模型,在脉冲免疫接种和垂直传染条件下,分析了其全局动力学行为.利用频闪映射,获得了无病周期解,给出了此周期解的全局吸引性,并获得了系统一致持续生存的条件.     

一类中立型脉冲时滞生物模型的正周期解(英文)

运用严格集压缩映射不动点定理,讨论得到了一类中立型脉冲时滞生物模型正周期解存在的充分条件.我们去掉了文[6,7,12-14]周期解存在的一些条件,推广了对应的结果.     

食饵具有流行病的阶段结构捕食模型

本文考虑了一类食饵具有流行病和阶段结构的脉冲时滞捕食模型．利用脉冲时滞微分方程的相关理论和方法，获得易感害虫根除周期解全局吸引的充分条件以及当脉冲周期在一定范围内时，天敌与易感害虫可以共存且易感害虫的密度可以控制在经济危害水平E（EIL）之下．我们的结论为现实的害虫管理提供了可靠的策略依据．     

A delay SIR epidemic model with pulse vaccination and incubation times

In this paper, a new delay SIR epidemic model with pulse vaccination and incubation times is considered. We obtain an infection-free semi-trivial periodic solution and establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination and nonlinear incidence have significant effects on the dynamics behaviors of the model. Our results are illustrated and corroborated with some numerical experiments.     

Dynamics of a discretized SIR epidemic model with pulse vaccination and time delay

We derive a discretized SIR epidemic model with pulse vaccination and time delay from the original continuous model. The sufficient conditions for global attractivity of an infection-free periodic solution and permanence of our model are obtained. Improving discretization, our results are corresponding to those in the original continuous model.     

Dynamics of a discretized SIR epidemic model with pulse vaccination and time delay

We derive a discretized SIR epidemic model with pulse vaccination and time delay from the original continuous model. The sufficient conditions for global attractivity of an infection-free periodic solution and permanence of our model are obtained. Improving discretization, our results are corresponding to those in the original continuous model.     

The differential susceptibility SIR epidemic model with time delay and pulse vaccination

The differential susceptibility SIR epidemic model with time delay and pulse vaccination is introduced. Some sufficient conditions for the globally attractivity of infection-free periodic solution and permanence of this system are presented. Two numerical simulations are also given to illustrate our main results.     

具饱和传染率的脉冲免疫接种SIRS模型

研究了具饱和传染率的脉冲免疫接种SIRS模型的一致持续生存和周期解,得到了无病周期解全局渐近稳定的充分条件和系统一致持续生存的充分条件,并应用分支理论得到了正周期解存在的分支参数.     

Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination

The dynamical behavior of an SIR epidemic model with birth pulse and pulse vaccination is discussed by means of both theoretical and numerical ways. This paper investigates the existence and stability of the infection-free periodic solution and the epidemic periodic solution. By using the impulsive effects, a Poincaré map is obtained. The Poincaré map, center manifold theorem, and bifurcation theorem are used to discuss flip bifurcation and bifurcation of the epidemic periodic solution. Moreover, the numerical results show that the epidemic periodic solution (period-one) bifurcates from the infection-free periodic solution through a supercritical bifurcation, the period-two solution bifurcates from the epidemic periodic solution through flip bifurcation, and the chaotic solution generated via a cascade of period-doubling bifurcations, which are in good agreement with the theoretical analysis.     

具有脉冲接种的DS-I-R传染病模型的定性分析

研究了具有脉冲接种的多易感群体的DS-I-R传染病模型,分析了该模型无病周期解的存在性,给出了对疾病传播有重要影响的基本再生数,得到了无病周期解全局稳定性的充分条件.     

Analysis of a viral infection model with delayed immune response

It is well known that the immune response plays an important role in eliminating or controlling the disease after human body is infected by virus. In this paper, we investigate the dynamical behavior of a viral infection model with retarded immune response. The effect of time delay on stability of the equilibria of the system has been studied and sufficient condition for local asymptotic stability of the infected equilibrium and global asymptotic stability of the infection-free equilibrium and the immune-exhausted equilibrium are given. By numerical simulating,we observe that the stationary solution becomes unstable at some critical immune response time, while the delay time and birth rate of susceptible host cells increase, and we also discover the occurrence of stable periodic solutions and chaotic dynamical behavior. The results can be used to explain the complexity of the immune state of patients.     

The dynamics of an impulsive delay SI model with variable coefficients

An impulsive delayed SI model with variable coefficients and a nonlinear incidence is formulated and analyzed. By introducing three thresholds, we obtain sufficient conditions for eradication and permanence of the disease, respectively. It is shown that the conditions depend on time delay for both the global attractivity of the positive infection-free periodic solution and permanence of the model. Furthermore, our results indicate that the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value. The main feature of this paper is that we introduce multi-delays and variable coefficients into the SI model, and exhibit a new method which is applied to investigate this model. Numerical results show that the system we considered has complex dynamics including periodic and quasi-periodic oscillations.     

一类具有非线性传染率的脉冲免疫接种的SIRSV模型

研究了具有非线性传染率的脉冲免疫接种SIRSV模型,得到了模型无病周期解全局渐近稳定的充分条件和系统持续生存的充分条件.