脉冲泛函微分方程的渐近稳定性

讨论了一类脉冲泛函微分方程的渐近稳定性.通过改进 Liapunov泛函的上界,利用Liapunov泛函第二方法和Jensen不等式,得到了一个一致稳定性定理和一个一致渐近稳定性定理,给出的例子说明了所得结果的优越性.     

无穷时滞脉冲方程的一致渐近稳定性

本文利用Liapunov泛函与Liapunov函数方法建立了无穷时滞脉冲泛函微分方程基于两种测度的一致稳定和一致渐近稳定的一个新的定理,并通过实例说明了所获结论的应用.     

中立型泛函微分方程中Liapunov泛函的Razumikhin型定理

本文借助Liapunov泛函附加Razumikhin条件,研究了中立型泛函微分方程解的一致渐近稳定性,统一了Liapunov泛函方法和Razumikhin技巧,所得的结果推广了文[4—8]中的工作。     

带有延迟脉冲量的脉冲随机微分方程的稳定性（英文）

本文研究带有限延迟脉冲随机泛函微分方程的p阶矩稳定性和p阶矩渐近稳定性的问题.利用Razumikhin技巧和Lyapunov函数的方法,获得方程p阶矩稳定性和p阶矩渐近稳定性的结果.     

具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用 D算子的某些性质及 Liapunov泛函的方法 ,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性 ,得到了新的结果 .     

具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用D算子的某些性质及Liapunov泛函的方法,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性,得到了新的结果。     

抽象泛函微分方程Ⅱ稳定性的一次近似准则

本文研究一类抽象泛函微分方程的解的渐近性质,我们利用Liapunov泛函建立了若干稳定性的判别准则。     

脉冲无限时滞微分方程零解的一致渐近稳定性

利用Liapunov泛函和改进的Razumikhin技巧讨论了脉冲无限时滞微分方程零解的一致渐近稳定性,推广和改进了已有文献的结果.     

随机中立型泛函微分方程的稳定性态

给出了一类中立型随机泛函方程的随机一致稳定性的充分条件,利用了新的分析技巧处理中立型时滞项,得到了中立型随机时滞泛函微分方程渐近稳定性的充分判据.在处理各种渐近估计是有效的.     

脉冲积分——微分方程的几个渐近稳定性结果

本文运用 Liapunov泛函法对于在可变时间具有脉冲扰动的 Volterra型泛函微分方程建立几个渐近稳定性结果 .它们与关于脉冲常微分方程、积分微分方程的已有结果的区别在于更着重反映脉冲对稳定性的影响     

Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.     

有界噪声参激一类三维系统的矩Liapunov指数

对于一类三维中心流形上受有界噪声参激的余维2分岔系统,计算了它的矩Liapunov指数．根据随机动力系统理论,首先建立了系统矩Liapunov指数求解的特征值问题,然后由奇异摄动法,得到了弱噪声展开的矩Liapunov指数的二阶渐近解析表达式和数值结果．接着进一步研究了有界噪声和系统参数对矩Liapunov指数和稳定指标的影响．结果表明:系统的随机稳定性有被有界噪声加强的可能性．     

On the mean square stability of linear difference equations

The mean square asymptotic stability of linear stochastic difference equations is studied. The Liapunov method of stability analysis is extended to stochastic difference equations, and several criteria for the mean square stability of the equilibrium state are established. Two examples of the application of the stability theorems are also considered.     

Fixed points and stability of neutral stochastic delay differential equations

In this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized.     

Stochastic Nonlinear Beam Equations with Lévy Jump

In this paper, we study stochastic nonlinear beam equations with Lévy jump, and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.     

一类差分方程的渐近性

本文对高维非自治差分方程x(τ+1)=f(τ,x)+g(τ,y);y(τ+1)=k(τ,x,y) (1)得到了保证其平凡解渐近稳定,一致渐近稳定的判别准则,而对V逐数的差分不要求负定性,推广了文[1]中相应的结果.     

Dynamical Analysis for a General Jerky Equation with Random Excitation

A general jerky equation with random excitation is investigated in this paper. Before introducing the random excitation term, the equation is reduced to a two-dimensional model when undergoing a Hopf bifurcation. Then the model with the parametric excitation and external excitation is converted to a stochastic differential equation with singularity based on the stochastic average theory. For the equation, its dynamical behaviors are analyzed in different parameters'' spaces, including the stability, stochastic bifurcation and stationary solution. Besides, numerical simulations are given to show the asymptotic behavior of the stationary solution.     

A SINGLE SPECIE MODEL WITH RANDOM PERTURBATION UNDER CONTRACEPTIVE CONTROL

In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded mean of solution is obtained by using the Liyapunov function and Chebyshev inequality. Lastly, stochastic global asymptotic stability of zero equilibriums is analyzed.     

二阶非线性微分方程零解的全局渐近稳定性

对于二阶非线性微分方程零解的全局渐近稳定性的研究,含一,二个非线性项的研究成果较多,非线性项在两个以上的研究成果较少,本文研究具有四个非线性项的问题,而具去掉了一般要求Liapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界。