一个具有时滞和反馈控制的单种群模型的全局稳定性

研究一个具有时滞和反馈控制的单种群模型,通过构造适当的Lyapunov泛函,得到了保证系统的一个正平衡点全局渐近稳定的充分条件,并对一个实例进行了数值模拟。     

具有连续分布时滞神经网络的稳定性分析

本文研究具有连续分布时滞神经网络的平衡点的稳定性问题,利用构造Ｌｙａｐｕｎｏｖ泛函和不等式分析技巧,给出了具有连续分布时滞神经网络全局渐近稳定性的充分条件。     

一类具有连续分布时滞模型的稳定性

本文利用一些分析技巧和Lyapunov泛函方法,研究一类具有连续分布时滞模型x'_i(t)=-b_ix_i(t) sumfromj=1to∞()ω_ijf_j(integralfromn=0to∞()k_j(s)x_j(t-s)ds) p_i,i=1,2,……,n平衡点的全局渐近稳定性,并获得了一个新的充分条件．     

具有阶段结构和免疫反应的病毒动力学模型的全局稳定性

研究了一类被感染细胞具有潜伏和活性两阶段以及免疫反应的病毒动力学模型.通过建立适当的Lyapunov泛函和使用LaSalle不变集原理,获得当σ≤1,ω≤1σ和σω1时,对应的未感染平衡点P,体液免疫未激活的无免疫感染平衡点M,体液免疫已激活的感染平衡点N是全局渐近稳定的充分条件.所获得结果推广了Nowak(1996)和Bangham(1997)的工作,得到了一些新结果.     

具有S-分布时滞BAM神经网络的全局指数稳定性

研究一类S-分布时滞BAM神经网络的稳定性问题.通过构造恰当的Lebesgue-Stieltjes积分型Lyapunov泛函,并结合Schwartz不等式和一些分析技巧,得到了系统全局指数稳定的充分条件,最后给出了主要定理的一个实例,表明结论的有效性.     

基于双时滞HTLV-I病毒模型的稳定性分析

针对双时滞HTLV-I病毒感染模型,探讨其平衡点及稳定性理论.依据模型固有属性,研究解的正性和有界性;通过构造适当Lyapunov泛函和利用稳定性理论,获证未感染平衡点和免疫耗尽平衡点是全局渐近稳定的;借助Hopf分支理论,分析免疫激活平衡点处相应特征方程具有的性质,获得该平衡点的局部稳定性和发生Hopf分支的充分条件.最后,数值实验结果表明,将HLTV-I模型中引入双时滞是合理的,有助于解释HTLV-I病毒的传播现象.     

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.     

一类具有CTL免疫和时滞的HTLV-I传染病模型的动力学性质(英文)

主要研究了一类具有CTL免疫和时滞的HTLV-I传染的数学模型.通过构造Lyapunov泛函,分别证明了当R₀≤1,R₁≤10,R1>1时,系统（1.1）的无病平衡点E₀,无免疫平衡点E₁及地方病平衡点E₂是全局吸引的.     

一类具有吸收效应和胞内时滞的HBV感染模型的全局稳定性（英文）

研究一类具有吸收效应和胞内时滞的HBV感染动力学模型.通过构造适当的Lyapunov泛函证明了当基本再生数小于1时,未感染平衡点是全局渐近稳定的;当基本再生数大于1时,给出了病毒感染平衡点全局渐近稳定的充分条件.     

Watkinson时滞差分方程模型的全局渐近稳定性

考虑差分方程ｘｎ＋１＝λｘｎ／（１＋ａｘｎ－ｋ）＾ｐ＋ｂλｘｎ－ｍ,ｎ＝０,１,２,…,其中ａ,ｂ,ｐ＞０,λ＞１,ｋ,ｍ∈｛０,１,２,…｝,当ｋ＝ｍ＝０时,Ｗａｔｋｉｎｓｏｎ用此方程来描述热带地区季蜀黍属作物的生长规律,当Ｐ＝１时,此方程就是著名的含多个滞量的Ｌｏｇｉｓｔｉｃ微分方程的离散模拟,本文主要目的是研究该方程唯一正平衡解的全局渐近稳定性。     

Dynamics of an HIV-1 therapy model of fighting a virus with another virus

In this paper, we rigorously analyse an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus. We show that when the basic reproduction ratio ?₀<1, then the infection-free equilibrium E ₀ is globally asymptotically stable; when ?₀>1, E ₀ loses its stability and there is the single-infection equilibrium E _s. If ?₀∈(1, 1+δ) where δ is a positive constant explicitly depending on system parameters, then the single-infection equilibrium E _s that is globally asymptotically stable, while when ?₀>1+δ, E _s becomes unstable and the double-infection equilibrium E _d comes into existence. When ?₀ is slightly larger than 1+δ, E _d is stable and it loses its stability via Hopf bifurcation when ?₀ is further increased in some ways. Through a numerical example and by applying a normal form theory, we demonstrate how to determine the bifurcation direction and stability, as well as the estimates of the amplitudes and the periods of the bifurcated periodic solutions. We also perform numerical simulations which agree with the theoretical results. The approaches we use here are a combination of analysis of characteristic equations, fluctuation lemma, Lyapunov function and normal form theory.     

Dynamics of an HBV model with diffusion and delay

In this paper we model and analyze the hepatitis B virus (HBV) infection in a diffusion model confined to a finite domain, induced by intracellular time delay between infection of a cell and production of new virus particles. The equilibrium solutions are obtained and the stability is analyzed if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion and intracellular time delay are obtained by computer simulations.     

Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.     

捕食者有无限时滞效应的两种群系统的全局渐近稳定性

本文用Liapunov泛函方法研究捕食者有无限时滞效应的捕食-被捕食系统的平衡状态的稳定性．文章提供了判定系统的平衡状态全局渐近稳定的简单条件,不要求积分核指数衰减.     

栓皮栎种群数量动态的谱分析与稳定性

1　前　言波动可出现于所有的植被中 ,而谱分析的方法可以揭示种群数量变动的周期性波动。Ｖｅｂｌｅｎ等通过老龄林结构和动态分析认为 :优势种的更替是周期循环的 ,而不是一个连续发展过程[2 ]。谱分析方法在昆虫数量动态研究中应用较多[1 ],在植物生态学研究中也有数例应用 ,伍业钢等[2 ]首次将之应用于阔叶红松林的演替与天然更新过程的研究 ,认为红松天然更新过程的周期波浪式发展 ,是其稳定的一个特点。但对于林木年龄较小、增长特征较明显的种群 ,谱分析方法是否适用 ,其结果与种群稳定性的关系如何 ,则尚未见报道。本文以河南省分布…     

The impact of maturation delay of mosquitoes on the transmission of West Nile virus

We formulate and analyze a delay differential equation model for the transmission of West Nile virus between vector mosquitoes and avian hosts that incorporates maturation delay for mosquitoes. The maturation time from eggs to adult mosquitoes is sensitive to weather conditions, in particular the temperature, and the model allows us to investigate the impact of this maturation time on transmission dynamics of the virus among mosquitoes and birds. Numerical results of the model show that a combination of the maturation time and the vertical transmission of the virus in mosquitoes has substantial influence on the abundance and number of infection peaks of the infectious mosquitoes.     

Global dynamics of a chemostat competition model with distributed delay

 We study the global dynamics of n-species competition in a chemostat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a fluctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured alone, we prove that at most one competitor survives. The winner is the population that has the smallest delayed break-even concentration, provided that the orders of the delay kernels are large and the mean delays modified to include the washout rate (which we call the virtual mean delays) are bounded and close to each other, or the delay kernels modified to include the washout factor (which we call the virtual delay kernels) are close in L ¹-norm. Also, when the virtual mean delays are relatively small, it is shown that the predictions of the distributed delay model are identical with the predictions of the corresponding ODEs model without delay. However, since the delayed break-even concentrations are functions of the parameters appearing in the delay kernels, if the delays are sufficiently large, the prediction of which competitor survives, given by the ODEs model, can differ from that given by the delay model. Received: 9 August 1997 / Revised version: 2 July 1998