A note on global attractivity of the periodic solution for a model of hematopoiesis

For the generalized periodic model of hematopoiesis $x^{\prime }\left(t\right)=-a\left(t\right)x\left(t\right)+\sum _{i=1}^m\frac{b_i\left(t\right)}{1+x{(t-{\tau }_i\left(t\right))}^n},$ with $0<n\le 1$, sufficient conditions for the global attractivity of its positive periodic solution are given, improving previous results in the literature. The effectiveness of the present criterion is illustrated by a numerical example.     

GLOBAL ATTRACTIVITY OF THE MODEL FOR THE SURVIVAL OF RED BLOOD CEELS WITH SEVERAL DELAYS

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｅｌａｙｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｄＮ（ｔ）ｄｔ＝－μＮ（ｔ）＋Ｐｅ－ｒＮ（ｔ－τ），ｔ≥０（１）ｗｈｅｒｅμ∈（０，１），ｐ，ｒａｎｄτ∈（０，∞）ｗａｓｕｓｅｄｆｉｒｓｔｂｙＷａｚｅｗｓｋａＣｚｙｚ...     

Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model

Sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive Lasota-Wazewska model for the survival of red blood cells.     

A Lotka-Volterra type food chain model with stage structure and time delays

A three-species Lotka-Volterra type food chain model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators (immature top predators) do not have the ability to feed on prey (predator). By using some comparison arguments, we first discuss the permanence of the model. By means of an iterative technique, a set of easily verifiable sufficient conditions are established for the global attractivity of the nonnegative equilibria of the model.     

某类差分方程零解的全局吸引性及其应用

研究差分方程△xn=r n f(x n-k)的全局吸引性），用二次迭代法导出方程的零解全局吸引的一族新的充分条件，将结果应用于Logistic差分方程及Michelis-Menten差分模型，所得推论改进了已有结果。     

PERMANENCE AND PERIODIC SOLUTION FOR NONAUTONOMOUS COMPETITION-PREDATOR SYSTEM WITH TYPE II FUNCTIONAL RESPONSE

A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.     

一类时滞反应扩散方程的稳态解的全局吸引性

本文研究了一类带扩散项造血生物模型当非线性项不具有单调性时,Dirichlet边值条件下稳态解的全局吸引性.     

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．     

Logistic型脉冲泛函微分方程零解的全局吸引性

本文研究Logistic型脉冲泛函微分方程满足初值条件x（t）=(?)（t）,t∈[g（0）,0],(?)∈PC（t）解的整体存在及全局吸引性,所获结果包含和改进了所有相关的已知结果.     

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．