具有饱和发生率的病毒感染模型的全局稳定性分析

讨论了一类具有饱和发生率的病毒感染数学模型,分析得到了无病平衡点和持续带毒平衡点的全局稳定性条件.当病毒感染的基本再生数R_01时,无病平衡点全局渐近稳定;当R_01时,持续带毒平衡点全局渐近稳定.     

变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。     

具阶段结构及比率依赖型捕食系统的Hopf分支与稳定性

本文研究了一类食饵具有阶段结构的比率依赖型捕食模型的稳定性和Hopf分支的存在性问题.通过分析相应的特征方程,得到了平衡点局部稳定的充分条件,并指出当时滞穿过某特定值时正平衡点出现Hopf分支.利用比较定理与迭代方法证明了正平衡点的全局渐近稳定性,得到正平衡点全局渐近稳定的充分条件.最后,举例说明所得结果的可行性.     

具有时滞和阶段结构的捕食-被捕食模型及最优捕获策略

研究了一个具有阶段结构和时滞的捕食-被捕食模型.分析了它的局部性质。得到某些非负平衡点全局稳定的充分条件,其中用到李雅普诺夫函数及其他方法．最后,在内部平衡点全局稳定的情况下,得出了最优捕获策略．     

一类具有非线性传染力的传染病模型的稳定性分析

研究了一类具有非线性发生率的急慢性阶段传染病模型,得到了确定模型全局动力性的阀值参数-基本再生数R_0,证明了R_01时,无病平衡点是全局渐近稳定的,疾病消失;若R_01,则存在地方病平衡点且是稳定结点,并证明了一定条件下地方病平衡点是全局渐近稳定的,疾病将蔓延.     

食饵有病的生态-流行病模型的稳定性研究

在考虑捕食者捕食染病的食饵对自身的不利作用的基础上建立了食饵有病的生态-流行病模型,得到了系统平衡点局部渐近稳定的充分条件;讨论了系统的非负不变性、解的有界性,并在此基础上研究了边界平衡点的全局稳定性,得到了平衡点全局稳定的充分条件。     

一类具有阶段结构和隔离的种群-传染病模型

该文讨论了一类具有阶段结构和隔离的种群-传染病模型.在该模型中,假设染病者没有生育能力.通过分析讨论,得到了地方病平衡点存在的阈值条件,以及无病平衡点和地方病平衡点局部渐近稳定和全局渐近稳定的充分条件.     

捕食者具有流行病的捕食-被捕食(SI)模型的分析

建立并分析了捕食者具有疾病的生态-流行病(SI)模型,讨论解的有界性,得到了平衡点局部渐近稳定的充分条件,进一步,分析了平衡点的全局稳定性,得到了捕食者绝灭和疾病成为地方病的充分条件．     

一类中立型Hopfield神经网络的全局吸引集

讨论了中立型Hopfield神经网络模型,利用矩阵谱的性质和微分不等式分析等技巧,给出了其不变集和全局吸引集的判别准则．特别地,当系统有平衡点时,我们也得到了平衡点全局稳定的判别条件．     

具有饱和发生率和免疫响应的病毒感染模型的稳定性分析改进

通过构造Lyapunov函数,改进了具有饱和发生率和免疫响应的病毒感染数学模型的稳定性分析,得到了当病毒感染的基本再生数R_01时,无病平衡点全局渐进稳定;当R_01时,在一定条件下,免疫耗竭平衡点和持续带毒平衡点全局渐近稳定的结论.     

Existence, multiplicity and stability of endemic states for an age-structured S-I epidemic model

We study an S-I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with two endemic equilibria is shown. Finally, we analyse numerically how the stability of the endemic equilibrium is affected by the extra-mortality and by the possible periodicities induced by the demographic age-structure.     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.     

具有年龄结构的接种流行病模型正平衡解的全局稳定性

研究一个具有年龄结构的接种SIS流行病模型正平衡解的稳定性,先利用等价积分方程给出了正平衡解存在的充分条件,再利用迭代方法及函数的单调性,得到了零平衡解与正平衡解全局稳定的充分条件。     

A stage-structured predator–prey model with distributed maturation delay and harvesting

ABSTRACT

A stage-structured predator–prey system with distributed maturation delay and harvesting is investigated. General birth and death functions are used. The local stability of each feasible equilibria is discussed. By using the persistence theory, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functional and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when the other equilibria are not feasible, and that the boundary equilibrium is globally stable if the coexistence equilibrium does not exist. Finally, sufficient conditions are derived for the global stability of the coexistence equilibrium.     

区间多种群Volterra生态系统的全局稳定性

讨论了区间多种群Volterra生态系统正平衡点的全局渐近稳定性,对于互惠型区间多种群Volterra生态系统不仅给出了正平衡点的全局稳定的充分必要条件,而且给出了系统存在平衡点的充分条件,对于一般的区间多种群Volterra生态系统给出了正平衡点全局稳定的充分条件。     

Immune network behavior—I. From stationary states to limit cycle oscilations

We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.     

三种群合作系统的全局渐近性态

考虑三种群合作系统:dχi/dt=χi(b-∑j3=1αijχj),χi(0)>0,b>0,αij<0,i≠j,i,j=1,2,3,完整地分析了其全局渐近性态:证明了该系统不存在闭轨,给出了正平衡点存在且全局渐近稳定的充要条件,证明了若系统不存在正平衡点,则所有解均趋于无穷.     

时滞Logistic型差分方程的振动及稳定性

本文获得了如下Xn 1=xnexp(a bxn-k^p-cxn-1^q）时滞Logistic型差分方程所有正解关于其平衡点振动的充要条件，同时还获得了一个正平衡点渐近稳定的充分条件，其中A∈（0，∞），B∈（-∞，O]，C∈（0，∞），K,l∈N。