一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

时滞BAM神经网络模型的稳定性分析

本文研究了一个含有n+1个神经元的多时滞BAM型神经网络模型.利用儒歇定理及其推论分析了该动力特征方程根的分布情况,进而得到动力系统稳定和Hopf分支存在的条件,画出了分支图.研究了该动力系统的Pitchfork分支,得到了Pitchfork分支曲线,讨论了在分支曲线的不同区域里平衡点的稳定性.     

一类具有暂时免疫传染病模型的Hopf分支

本文应用Hassard的“规范形”方法,讨论了一类具有暂时免疫传染病模型的动力形态．给出了该系统发生Hopf分支的参数曲线,进一步计算出了决定分支方向及稳定性的参数条件,并给出了生态解释．     

一类Hodgkin-Huxley模型的分支研究

考虑一类描述肌细胞膜电位变化的Hodgkin-Huxley模型的分支问题.利用常微分方程的分支理论,结合数值模拟结果,对模型的单参数分支与双参数分支进行了讨论.分析了Bogdanov-Takens分支,得到了相应的鞍结点分支曲线,Hopf分支曲线与同宿分支曲线.     

一类时滞神经网络模型的稳定性与全局Hopf分支

研究了一类由两个神经元构成的时滞神经网络模型的稳定性和局部Hopf分支,并结合一般泛函微分方程的全局Hopf分支定理,利用度理论研究了全局Hopf分支的存在性．     

蕨类植物rbcL基因正选择和负选择位点的鉴定

基于分支模型、位点模型及分支-位点模型对蕨类的rbcL基因所受到的选择压力进行了分析.结果显示:分支模型下检测到大部分分支处于负选择,仅4个分支处于正选择压力下,并且仅2分支具有统计上的显著性;在位点模型下,通过比较模型M1a/M2a和M7/M8,在氨基酸水平上模型M2a和模型M8均鉴定出98L位点被正选择;在模型M8下,鉴定负向选择位点共228个,占总序列的83.82%,从而揭示出负选择对rbcL基因的进化起着非常重要的作用;在分支位点-模型c下鉴定出262A被正选择.98L、262A位点分别位于rbcL羧基末端α/β桶结构域的第3和第8个α螺旋上.蕨类通过该结构域的适应性进化,适应白垩纪被子植物兴起而引发的陆地生态系统改变,研究结果为以后实验分析提供了首选位点.     

三种竞争种群的古典Gause-Lotka-Volterra系统

本文讨论了三种竞争种群的古典GLV系统．对系统所有非负平衡点的稳定性,进行了分析,给出了正平衡点全局稳定的充分条件,应用Hopf分支定理,我们给出了系统具有分支值的充分条件．     

一类具时滞和非线性发生率的生态流行病模型的稳定性和Hopf分支

研究一类具有时滞和非线性发生率的生态流行病模型.以滞量为参数,通过分析特征方程,得到了正平衡点局部稳定和Hopf分支存在的条件.同时,应用中心流形定理和规范型理论,得到了分支方向和分支周期解的稳定性计算公式.最后对所得理论结果进行了数值模拟.     

念珠藻属植物nifH基因的适应性进化分析

念珠藻(Nostoc)固氮过程关键在于固氮酶的催化,而固氮酶复合物中的铁蛋白(NifH)是由高度保守的nifH基因编码的,该基因是进化史上现存最古老的功能基因之一。该研究选取念珠藻属及近缘类群的nifH基因序列共40条,采用最大似然法构建系统发育树;运行PAML4.9软件,对nifH基因编码蛋白进行生物信息学分析,并使用分支模型、位点模型和分支-位点模型检测该基因的选择位点,探讨nifH基因的适应性进化特征。结果表明:(1)最大似然树显示内类群中该研究物种共分为6个分支(A、B、C、D、E和F),其中D和E是2个大的分支,每个大分支中又各包含2个特殊的小分支A、F和B、C,其中F分支包含新疆古尔班通古特沙漠采集到的9株念珠藻,A分支包含F分支及该研究测定序列的4株葛仙米,B分支包含本研究测定序列的4株地皮菜和3株未定种的念珠藻,C分支包含NCBI数据库中下载的5株念珠藻、鱼腥藻序列和本研究测定序列的1株念珠藻。(2)在所分析的3种进化模型中,仅通过分支-位点模型检测出14个统计学上显著的正选择位点,即1F、2S、3S、4T、5A、6F、7F、8I、9S、10C、17I、27Y、29D和31R位点,表明念珠藻属植物的nifH基因发生了适应性变化,分支-位点模型是研究藻类基因适应性进化较好的模型。     

一个离散单种群动力系统的超临界Flip分支和Hoph分支(英文)

文中考虑一个非线性的具有年龄阶段结构的单种群离散模型,致力于揭示该系统的动力学行为,说明了系统在分支阈值附近会出现超临界Flip分支和Hoph分支.与一些文献不同的是文中用数学工具给出证明过程而不是用数值模拟的结果说明.     

非线性红松林生态系统的定性与分支研究(英文)

利用系统分析的方法研究了一类非线性红松林生态系统的稳定性,讨论了其鞍结分支和Hopf分支,且对Hopf分支周期解进行了详细的分析和计算,指出了红松林生态系统中松籽、鼠类和幼苗三种群数量具有周期波动的特征.     

具有稀疏效应的Predator-Prey模型的分支问题

讨论了具有稀疏效应的捕食－食饵模型的分支问题,并利用Ｈｏｐｆ分支理论和分界线环分支理论,得到了有多个极限环的结果。     

具HollingⅡ类功能反应的多时滞捕食-食饵系统的全局性质

本文研究了一类具HollingⅡ功能反应的捕食-食饵系统,首先用Cook等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统的正平衡点的稳定性及局部Hopf分支．进而,再结合吴建宏等人的用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支的存在性．     

Periodicity in an epidemic model with a generalized non-linear incidence

We develop and analyze a simple SIV epidemic model including susceptible, infected and perfectly vaccinated classes, with a generalized non-linear incidence rate subject only to a few general conditions. These conditions are satisfied by many models appearing in the literature. The detailed dynamics analysis of the model, using the Poincaré index theory, shows that non-linearity of the incidence rate leads to vital dynamics, such as bistability and periodicity, without seasonal forcing or being cyclic. Furthermore, it is shown that the basic reproductive number is independent of the functional form of the non-linear incidence rate. Under certain, well-defined conditions, the model undergoes a Hopf bifurcation. Using the normal form of the model, the first Lyapunov coefficient is computed to determine the various types of Hopf bifurcation the model undergoes. These general results are applied to two examples: unbounded and saturated contact rates; in both cases, forward or backward Hopf bifurcations occur for two distinct values of the contact parameter. It is also shown that the model may undergo a subcritical Hopf bifurcation leading to the appearance of two concentric limit cycles. The results are illustrated by numerical simulations with realistic model parameters estimated for some infectious diseases of childhood.     

Bifurcation analysis of the Nowak-Bangham model in CTL dynamics

This paper investigates the local bifurcations of a CTL response model published by Nowak and Bangham [M.A. Nowak, C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74]. The Nowak-Bangham model can have three equilibria depending on the basic reproduction number, and generates a Hopf bifurcation through two bifurcations of equilibria. The main result shows a sufficient condition for the interior equilibrium to have a unique bifurcation point at which a simple Hopf bifurcation occurs. For this proof, some new techniques are developed in order to apply the method established by Liu [W.M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl. 182 (1) (1994) 250]. In addition, to demonstrate the result obtained theoretically, some bifurcation diagrams are presented with numerical examples.     

Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling

In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh–Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.     

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.     

Stability of periodic solutions for a model of genetic repression with delays

A technique is discussed for locating the Hopf bifurcation of an n-dimensional system of delay differential equations which arises from a model for control of protein biosynthesis. Certain parameter values are shown to allow a Hopf bifurcation to periodic orbits. At the Hopf bifurcation the periodic orbits are shown to be stable either analytically or numerically depending on the parameter values.On leave from North Carolina State University.Supported in part by N.S.F. Grant # MCS 81-02828