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.     

具有潜伏和隔离的传染病模型的全局稳定性

研究了一类具有隔离仓室和潜伏仓室的非线性高维自治微分系统SEQIJR传染病模型,得到疾病绝灭与否的阀值一基本再生数R0．证明了当R0≤1时,模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的,疾病最终绝灭;当R0〉1时,模型存在两个平衡点,无病平衡点不稳定,地方病平衡点全局渐近稳定,疾病将持续．隔离措施影响着基本再生数,进而推得结论：适当地增大隔离强度,将有益于有效地控制疾病的蔓延．这就从理论上揭示了隔离对疾病控制的积极作用．     

一类谣言传播模型的全局稳定性

本文提出了一类具有媒体效应和标准传播率的谣言传播模型.基于谣言的基本再生数,分析了边界平衡点和正平衡点的存在性.利用Lyapunov-LaSalle不变集原理证明了边界平衡点的全局渐近稳定性,根据Routh-Hurwitz判据和广义Bendixson-Dulac定理证明了正平衡点的全局渐近稳定性.结果表明,媒体效应虽无法消除谣言,但能减小谣言传播的最终规模.数值例子验证了结论的有效性.     

一类差分方程解的全局吸引性

考虑差分方程xn+1=αxn/(1+k∑i=1βixn-i),n=0,1,2,….其中α∈(1,∞)且β=k∑i=1βi>0,k∈{0,1,2,…}.获得了使方程的正平衡点X=(α-1)/β为全局吸引的新充分条件     

具有常数输入及非线性发生率的SIQR传染病模型

讨论一类具有常数输入及非线性发生率的SIQR传染病模型,给出了疾病是否流行的阈值R₀=1.当R₀<1时,系统的唯一无病平衡点是全局渐近稳定的;当R₀>1时,系统有两个地方病平衡点,利用特征根法讨论了这两个地方病平衡点的稳定性,得出在某些参数范围内会出现Hopf分支现象;当R₀=1时,系统有唯一的地方病平衡点,利用中心流形定理证明了该地方病平衡点是不稳定的.     

带有外来流入人口和快慢反应的肺结核模型研究

本文研究了一个带有外来流入人口和快慢反应的SEIR肺结核模型,理论分析表明,只有外来潜伏者输入W_E=0时存在无病平衡点,当基本再生数R_O1时,无病平衡点全局渐近稳定。当R_O1时,无病平衡点不稳定.系统存在唯一的渐近稳定的地方病平衡点.最后通过数值模拟验证了理论结果,并且发现外来流入潜伏者和快慢反应参数对于不同流入人口系统的影响存在显著差异.     

具有连续接种和脉冲接种的SIVR模型研究

考虑了具有连续接种和脉冲接种的SIVR传染病模型,得到了模型的基本再生数.对于连续接种模型,证明了当基本再生数R_0~c≤1时无病平衡点是全局稳定的;当R_0~c1时,无病平衡点是不稳定的,模型存在地方病平衡点,并且当δ=0时,地方病平衡点是全局渐近稳定的.对于脉冲接种模型,得到了无病周期解的存在性和稳定性.最后,对连续接种和脉冲接种进行了比较.     

一类具有性传播的HIV/AIDS模型全局稳定性分析（英文）

本文,我们研究了一类同时考虑异性之间传播和同性之间传播以及具有常数输入的艾滋病传播模型.首先讨论了系统解的正性,平衡点的存在性等基本性质.利用比较原理证明了无病平衡点E_0的全局渐近稳定性.证明地方病平衡点的全局渐近稳定性时,我们用到了几何方法.最后使用MATLAB和取自南昌市东湖区数据进行了数值模拟,验证了结论的正确性并预测了该地区艾滋病人数的变化趋势.     

具有Crowley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性（英文）

本文讨论了一类具有Growley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性.利用Lyapunov函数和LaSalle不变原理证明:当基本再生数R_0≤1时,无病平衡点全局渐近稳定;当基本再生数R_01且免疫基本再生数R_0≤1时,免疫平衡点全局渐近稳定;当R_01时,地方病平衡点全局渐近稳定.     

具反馈控制的时滞阶段结构种群模型的稳定性

研究具反馈控制的时滞阶段结构种群模型,证明了正平衡点的局部渐近稳定性, 并给出了正平衡点全局渐近稳定的充分条件．     

n阶食物链反馈控制系统的稳定性与永久持续生存

本文研究了n阶食物链反馈控制系统的稳定性与永久持续生存问题，分别得到了该系统无反馈与有反馈两种情况下存在唯一正平衡点和永久持续生存的几个充要条件。文末的例子表明，本文在无反馈情况下的结果比现有的结果简单，有效，在有反馈情况下的结果填补了目前这一问题的空白。     

Global asymptotic stability of density dependent integral population projection models

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable 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。     

The principle of homeostasis in the hypothalamus-pituitary-adrenal system: new insight from positive feedback

Feedback control, both negative and positive, is a fundamental feature of biological systems. Some of these systems strive to achieve a state of equilibrium or "homeostasis". The major endocrine systems are regulated by negative feedback, a process believed to maintain hormonal levels within a relatively narrow range. Positive feedback is often thought to have a destabilizing effect. Here, we present a "principle of homeostasis," which makes use of both positive and negative feedback loops. To test the hypothesis that this homeostatic concept is valid for the regulation of cortisol, we assessed experimental data in humans with different conditions (gender, obesity, endocrine disorders, medication) and analyzed these data by a novel computational approach. We showed that all obtained data sets were in agreement with the presented concept of homeostasis in the hypothalamus-pituitary-adrenal axis. According to this concept, a homeostatic system can stabilize itself with the help of a positive feedback loop. The brain mineralocorticoid and glucocorticoid receptors-with their known characteristics-fulfill the key functions in the homeostatic concept: binding cortisol with high and low affinities, acting in opposing manners, and mediating feedback effects on cortisol. This study supports the interaction between positive and negative feedback loops in the hypothalamus-pituitary-adrenal system and in this way sheds new light on the function of dual receptor regulation. Current knowledge suggests that this principle of homeostasis could also apply to other biological systems.     

资源与资源利用者的脉冲收获控制

研究一类资源以Cui-Lawson增长为基础的具有状态依赖脉冲收获的生态系统.首先对无脉冲作用的系统进行定性分析,得到正平衡点存在和稳定的充分条件.其次对具有状态依赖的脉冲系统,利用微分方程几何理论中后续函数法得到系统的阶一周期解存在的充分条件,证明该周期解是轨道渐近稳定的,同时利用数值模拟讨论了系统生态意义.     

Expanding on Watson's framework for classifying patches: when is an island not an island?

Aim The aims were: (1) evaluate the potential of Watson's framework for studying species composition in fragments and islands for a specific landscape type: cryptobiotic crust systems in the arid south‐western US; (2) expand Watson's original model to include ephemeral/non‐equilibrium systems by revising his categories of patch age and matrix contrast; and (3) examine the interplay between patch dynamics and species autecology, demonstrating the need for more work on ephemeral patchy systems. Location Cryptobiotic crust systems in two piñon‐juniper sites in Central New Mexico, western North America. Results Watson's patch age designation was not applicable to our system because of its ephemeral or non‐equilibrial nature. Based on this result, we constructed what we refer to as a ‘speed key’ that includes equilibrium and non‐equilibrium patches of all kinds. For this model we maintained one of Watson's original traits: patch origin, and amended two others to describe persistence and permeability across the matrix. Importantly, persistence and matrix permeability must be evaluated as functions of the organisms under consideration. Systems that may be in equilibrium for one taxon may well be non‐equilibrial (ephemeral) for another. A patch that appears to be in high contrast with its intervening matrix may actually be in low contrast, depending on the dispersal ability of the organism through that matrix. Main conclusions To improve substantially on our understanding of patchy systems (whether islands or fragments) it is important to account explicitly for relevant organismal life‐history traits in the designation of those systems. Too often, patches are defined by how the researcher views them from his/her own spatio‐temporal viewpoint. Once we move to an organism‐centred understanding of these patches we may find surprising and novel comparisons that allow us to move across scales and inform our view of ecological patterns and processes. By incorporating non‐equilibrium systems into a model of insularity, this work has general implications that go beyond the scope of cryptobiotic crusts to add to the current dialogue in biogeography.     

Cooperativity of ligand binding as a function of monomer-dimer equilibrium parameters and acceptor concentration

A general monomer-dimer equilibrium system involving ligand interactions ispresented. Cooperativity features of specific limited models are analyzed by selecting the appropriate family of equilibrium constants from this general scheme. Each system is then characterized in terms of Hill coefficient dependency on alterations in values of equilibrium constants and total acceptor concentration. This method permits comparison of predicted cooperativity trends between systems. Contrasting reports concerning cooperativity dependencies for certain defined equilibrium systems are compared and the discrepancies resolved. Characteristics of cooperativity binding patterns are shown to include symmetry about dimerization association constant values, both positive and negative cooperativity for a single set of parameters, and significant changes in cooperativity features with relatively small changes in equilibrium parameters.     

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。     

Studies on assortative mating. III. The effects of incomplete penetrance in assortative mating systems

Four models of positive and negative assortative mating systems, exclusive or partial, in relation to phenotypes determined by a pair of autosomal alleles with dominance but with incomplete penetrance of the dominant allele in heterozygous state, are presented. By introducing the parameter of incomplete penetrance in the models of assortative matings, matings between individuals with identical genotypes will occur within the negative systems, as well as matings between individuals with different genotypes within the positive assortative mating systems. Thus, incomplete penetrance has the effect of retarding equilibrium on an assortative mating system, making this equilibrium equivalent to a system with a lower degree of assortative mating, where the penetrance equals 1 or 0. Another conclusion of biological interest drawn from the mathematical analysis presented in this paper is that for any value of the penetrance, the frequency of 0.5 for recessive individuals is also typical of exclusive or partial negative assortative mating systems at equilibrium.     

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。