一类具有脉冲效应的浮游生物模型的持久性以及概周期解

利用脉冲微分方程的对比定理以及李雅普诺夫函数法,我们研究了一类具有脉冲效应的浮游生物模型的持久性以及概周期解.文中所得结论改进了以往的研究成果.文中所用的研究方法可以用来研究其他带有脉冲的生物数学模型的持久性以及概周期解.最后,我们总结阐述了脉冲如何影响模型的持久性,概周期解以及一致渐进稳定性.     

Logistic种群演化模型的渐近加权周期性

在生态动力学研究中,研究者们往往假设环境因素f(t)随着季节变化而发生周期性变化.但是诸如光照等因素在这-年的变化都将有别于上-年.因此环境的变化不是严格周期的,从而f(t+T)=w(t)f(t),这里的w(t)≠1.在我们前期工作中称这类函数为加权周期函数.本文针对Logistic种群演化模型研究了这-情况,得到了-个有趣的结果:当内禀增长率和种内竞争率都发生加权周期变化时,种群演化会呈现出某种渐近加权周期性,而且其权函数刚好是种内竞争率权函数的倒数.这很好地解释了-个生态学现象:种内竞争加剧则意味着种群数量加快下降.     

一类浮游生物植化相克时滞抛物方程的稳态解

本文研究了水生生态系统中种群间能产生抑制毒素的Volterra竞争模型,用上下解的方法讨论了稳态解的渐近行为,得到了系统存在唯一全局稳定正稳态解的充分条件.     

一类竞争——合作生态模型平衡点的渐近稳定性

研究一类竞争-合作生态数学模型平衡点的渐近稳定性,得到了一组保证平衡点渐近稳定的充分条件.     

Asymptotic Behavior on a Competition Model Arising from an Unstirred Chemostat

This paper is concerned with the unstirred chemostat model with two-species and one non-reproducingresource.The global attractivity of the positive steady-state solutions of the original system is established.Moreover,the effects of the growth rate on the unique positive equilibrium of the single population model arestudied.     

Asymptotic Periodicity of Primes Associated to Multigraded Modules

In this paper, we investigate the asymptotic behavior of the set of primes associated to a graded ring extension of Noetherian multigraded rings and modules, and prove that the periodicity occurs in a cone. We also prove the same asymptotic behavior of the grade. The previous known results on this subject are recovered as a special case.     

有离散时滞的扩散Logistic方程的渐近周期性(英文)

在这篇文章中 ,我们主要研究具有离散时滞的扩散Logistic方程的渐近周期性 .对于系数具有周期性时 ,我们给出了渐进周期解存在并且唯一的必要条件 .     

Compactness in Spaces of Vector Valued Continuous Functions and Asymptotic Almost Periodicity

We characterize the precompact sets in spaces of vector valued continuous functions and use the resulting criteria to investigate asymptotic behaviour of such functions defined on a halfline. This problem arose in the context of a qualitative study of solutions to the abstract Cauchy problem. We give particular consideration to the relationship between vector valued asymptotically almost periodic functions on a subinterval [α, ∞] of the real line and precompactness of the set of its translates. Our compactness criteria are also applied to a question concerning the approximation property for spaces of vector valued continuous functions with topologies induced by weighted analogues of the supremum norm. as well as to obtain nonlinear variants on factorization of compact operators through reflexive Banach spaces.     

离散模型解的收敛性与周期性

The discrete-time network model of two neurons with function f(u)= {1,u∈[0,σ] 0,u ■[0,σ]is considered.We obtain sufficient conditions that solution of system is convergent or periodic.     

松弛模型中的液气共存平衡态

对密闭的一维有限长管道里的等温相变．研究了松弛模型中液气共存平衡态的稳定性．使用匹配渐近展开形式上推出了一阶扰动满足的线性系统．理论分析发现．初始小扰动通常会被耗散掉,然而在一些特殊情况下,它们会维持在一定的水平上．数值计算也表明了松弛机制对相变演化具有稳定作用．     

Dynamics of a Model of Allelopathy and Bacteriocin with a Single Mutation

In this paper we discuss a model of allelopathy and bacteriocin in the chemostat with a wild-type organism and a single mutant. Dynamical properties of this model show the basic competition between two microorganisms. A qualitative analysis about the boundary equilibrium, a state that microorganisms both vanish, is carried out. The existence and uniqueness of the interior equilibrium are proved by a technical reduction to the singularity of a matrix. Its dynamical properties are given by using the index theory of equilibria. We further discuss its bifurcations. Our results are demonstrated by numerical simulations.     

一个半参数回归模型的渐近正态性

考虑半多数回归模型yi＝xiβ＋g（xi）＋εi，lin，这里xi是具有已知方差σ的独立同分布随机样本，εi是具有零均值和有限方基σ2的独立同分布随机误差．β，g和εi的分布密度是未知的．本文作者构造了一个具有更小渐近方差的β的一个渐近正态估计．     

一个部份自回归模型的渐近有效性<英>

本文考虑部分自回归模型 X_t=X_(t-1)β g(U_t) ε_t,t≥1.这里g是一未知函数,β是一待估参数,ε_j是具有0均值和方差σ~2的i.i.d.误差,U_t i.i.d.服从[0,1]上均匀分布.本文首先给出了相合估计的收敛阶和Takeuchi意义下渐近有效界.同时给出了β最小二乘估计是有效的充要条件.最后证明了MLE是渐近有效的.     

Almost Periodicity for a Nonautonomous Discrete Dispersive Population Model

In this article, study the almost periodic profile of solutions for nonautonomous difference equations in Banach spaces. We apply our results in population dynamics.     

一类具有扩散的捕食模型的共存解

该文讨论了具有扩散的捕食模型.利用上下解方法和分支理论,得到了椭圆系统的共存解的存在性,并且讨论了共存解的稳定性.     

时间周期的离散SIS模型的传播动力学北大核心CSCD

该文研究了一类具有时间周期的空间离散多种群SIS模型的传播力学.首先,借助周期单调半流的传播速度与行波理论,证明了渐近传播速度c*的存在性.其次,利用比较原理,证得了渐近传播速度即为单调周期行波解的最小波速.     

一类竞争系统的Hopf分岔及分岔周期解的稳定性

首先研究具有时滞的竞争三种群平衡点的存在性,接着应用特征方程,发现当τ穿过某些数时出现了Hopf分岔,并用规范型方法和中心流形定理得到Hopf分岔和分岔周期解的稳定性的计算公式.并举例当τ变化时该模型会出现混沌现象.     

Periodicity in a “Food-limited” Population Model with Toxicants and Time Delays

Abstract With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,westudy the global existence of positive periodic solutions of a "food-limited" population model with toxicants andtime delays.Some new results are obtained.