GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.     

EXPONENTIAL STABILITY OF DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH DELAYS

In this paper, a new sufficient condition for the global exponential stability of a unique equilibrium point of discrete-time cellular neural networks is given. It is shown that the condition relies on the feedback matrices and is independent of the delay parameter. Furthermore, this condition is less restrictive than those given in the literature.     

变时滞Hopfield神经网络的全局指数稳定性

本文研究了一类具有变时滞Hopfield神经网络的稳定性问题.利用时滞微分不等式方法,获得了几个关于该网络的全局指数稳定性与时滞无关的充分条件,并且给出了此类网络的收敛指数的估计,推广了已知文献的结果.最后给出数值例子证明结论的有效性.     

GLOBAL STABILITY OF AN SVIR EPIDEMIC MODEL WITH VACCINATION

In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable wh...     

EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

ＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＬＩＮＥＡＲＴＩＭＥ－ＶＡＲＹＩＮＧＩＭＰＵＬＳＩＶＥＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＤＥＬＡＹＳ￥ＧｕａｎＺｈｉｈｏｎｇ（关治洪）；ＬｉｕＹｏｎｇｑｉｎｇ（刘永清）（ＳｏｕｔｈＣｈｉｎａＵｎ...     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

具有垂直传染的年龄结构SEIR流行病模型的稳定性

本文讨论了一类具有垂直传染的年龄结构SEIR 流行病模型,运用有界线性算子半群理论证明了模型本身非负解的存在唯一性.运用微分方程及积分方程中的理论和方法, 研究了该模型平衡点的稳定性,得到了无病平衡点与地方病平衡点的稳定性条件.     

变时滞细胞神经网络的指数稳定的一个充分条件

本文我们研究了变时滞细胞神经网络的指数稳定性。利用分析技巧，获得了变时滞细胞神经网络的指数稳定的充分条件，改进了已有文献中的相应结果。     

具有垂直传染和接触传染的传染病模型的稳定性研究

本文研究了一类具有垂直传染和接触传染的传染病模型.利用常微分方程定性与稳定性方法,分析了该模型非负平衡点的存在性及其局部稳定性.同时,利用LaSalle不变性原理和通过构造适当的Lyapunov函数,获得了平凡平衡点、无病平衡点和地方病平衡点全局渐近稳定的充分条件.结果表明当基本再生数小于等于1时,所有种群趋于灭绝;当基本再生数大于1和病毒主导再生数小于1时,病毒很快被清除;当基本再生数大于1和病毒主导再生数大于1以及满足一定条件时,病毒持续流行并将成为一种地方病.     

具两个时滞项的微分方程的稳定性

本文考虑了一类具两个时滞项的微分方程的稳定性，其中一个时滞项的系数非负，另一个时滞项的系数非正．当非负系数恒为零时，本文所得结论改进了Yorke等提出的3/2稳定性定理的相应结论，当非负系数项的时滞为零，本文不同于已有文献用Liapunov函数或泛函法将时滞项作为干扰处理，而是反过来利用时滞项让方程稳定．