具可变种群总数的SIS传染病模型指数稳定性

本文研究了一类具可变种群总数的SIS传染病模型,利用基于比较原理的新的分析技巧,获得了一些无病平衡点和传染病平衡点全局和局部指数稳定的充分条件,同时得到了平衡点指数收敛率与指数收敛区域的估计.     

分离变量非线性系统的全局稳定性

借助Lyapunov函数方法 ,讨论了一类分离变量系统的全局稳定性和全局指数稳定性 ,得到了由系统自身特点所给出的几个显示代数判据 ,这些充分性结论为实际应用提供方便 ,推广了有关文献中的一些结果 .     

随机扰动下的增长模型

以确定性的Solow增长模型为背景,文章将随机扰动引入其中.因此模型中的要素方程从ODE过渡到It SDE,并对其作某些定性的分析.进而运用二次Liapunov函数等方法对随机Solow模型的零解的稳定性及其平稳分布进行了有益的探索,得出了一些有意义的结果.文章的主要结论是:随机干扰将实质性地改变由确定性增长模型所描述的经济增长路径.     

ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.     

Hopfield型时滞神经网络的指数稳定性

研究了Ｈｏｐｆｉｅｌｄ型随机时滞神经网络ｄｘ（ｔ）＝［－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ一τ））］ｄｔ＋ｆ（ｔ．ｘ（ｔ）,Ｘ（ｔ—τ））ｄｗ（ｔ）的均方指数稳定性与几乎必然指数稳定性．应用Ｌａｙａｐｕｎｏｖ函数与鞅不等式,建立了这种随机时滞神经网络指数稳定的时滞相关的充分条件．文献中某些关于确定性的时滞神经网络ｘ（ｔ）＝－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ－τ））与神经网络ｘ（ｔ）＝－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ））的稳定准则是文中的特殊情况．     

网络的模块矩阵及其社团结构指标

探讨了复杂网络的模块矩阵的正(负)特征谱与网络的社团结构(反社团结构)的关系,给出了反映网络社团结构性质的相关定义.利用模块矩阵的多个特征值与特征向量,引入反映个体对所处社团的依附程度一种结构中心化指标.利用人工网络与实际网络数据,将这种指标与几种经典的中心化指标进行了比较.结果表明该指标具有较好的分辨率并与度指标具有一定程度的相关性.     

中立型随机泛函微分方程的稳定性

该文研究了一般中立型随机微分方程解的渐近性质,利用Lyapunov函数和上鞅收敛定理,得到 了该方程解的一些渐近稳定性、多项式渐近稳定性及指数稳定性等渐近性质,其结果涵盖并 推广了已有文献的结论。     

A novel circuit design for complementary resistive switch-based stateful logic operations

Recently, it has been demonstrated that memristors can be utilized as logic operations and memory elements. In this paper, we present a novel circuit design for complementary resistive switch(CRS)-based stateful logic operations. The proposed circuit can automatically write the destructive CRS cells back to the original states. In addition, the circuit can be used in massive passive crossbar arrays which can reduce sneak path current greatly. Moreover, the steps for CRS logic operations using our proposed circuit are reduced compared with previous circuit designs. We validate the effectiveness of our scheme through Hspice simulations on the logic circuits.     

Robust stability of uncertain neutral linear stochastic differential delay system

The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.     

随机泛函微分方程的渐近稳定性

应用多个Liapunov函数讨论了随机泛函微分方程解的渐近行为,建立了确定这种方程解的极限位置的充分条件,并且从这些条件得到了随机泛函微分方程渐近稳定性的有效判据,使实际应用中构造Liapunov函数更为方便．同时也说明了该结果包含了经典的随机泛函微分方程稳定性结果为其特殊情况．最后给出的结果在随机Hopfield神经网络中的应用．