正则线性差分方程

<正> 1.引言H.Poincaré 与 O.Perron 研究了 Poincaré 型(以下简称 P 型)差分方程解的渐近特性,给出下面的定理 (Poincaré)假若 n 阶线性齐次差分方程y(x+n)+α_1(x)y(x+n-1)+…+α_n(x)y(x)=0 (x=0,1,2,…).(*)是 P 型的,即其系数 α_v(x)具有有限极限     

含有n个滞量的三维微分差分方程组周期解的存在性

本文研究含有n 个滞量的三维微分差分方程组x(t)=sum from i=1 to ∞(1/i)f[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]y(t)=sum from i=1 to ∞(1/i)g[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)](τ_i>0)z(t)=sum from i=1 to ∞(1/i)h[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]周期解的存在性,给出了方程组周期解周期的取值范围.推广并改进了文[1]的结果.     

一类非线性微分-差分方程解的殆指数渐近稳定性

对形如 x(t)=af(x(t))+ sum from i=1 to n (b_if_i(x(t-τ_i)))的微分-差分方程,给出了其零解殆指数渐近稳定的定义,得到了几个判定零解殆指数渐近稳定性的定理。     

一类Poincaré差分方程解的渐近性质

以二阶的情形讨论了Poincaré差分方程y(n m) (a1 p1(m))y(n m-1) … (an pn(m)y(m)=0当其常系数部分x(n m) a1x(n m-1) … anx(m)=0的特征方程有相同的根时，解的渐近性质，通过不动点方法给出了Poincaré差分方程的解渐近于其常系数方程解的条件，并给出了渐近式高阶项的估计。     

利用极限方程研究一类二阶方程的一致渐近稳定性

本文考虑二阶微分方程x+h(x,x,t)x+f(x)+g(x,x,t)=0或等价系统x=y y=-h(x,y,t)y-f(x)-g(x,y,t) (1)我们利用极限方程及其与不变性和稳定性理论的关系,提出原点O关于系统(1)为一致渐近稳定的充分必要条件。     

离散系统的渐近稳定性

先讨论吋变离散系统 (1) x(τ+1)=f(τ,x(τ),τ=t_0+k,k=0,1,2,…,t_0≥0。其中f:[0,∞)×D→R~n,D是R~n中包含原点的开集,f(τ,0)≡0。对每个t_0≥0和每个x_0∈D,保证(1)有唯一的解x(τ)=x(τ,t_0,x_0),具有x(t_0,t_0,x_0)=x_0。对于连续的时变系统来说,只有Liapunov函数V(t,x)正定和它关于系统的导数V(t,x)负定性是不能保证零解的渐近稳定性的,通常附加V具有无穷小上界,或限定方程右端函数F(t,x)对有界的|x|有界,或限定V(t,x)→∞,当t→∞,x≠0时才能推出零解的渐近     

一类时滞Lienard方程的一致有界及全局渐近稳定

给出时滞 Lienard方程 x″+f( x) x′+ax′( t-τ) +g( x( t-τ) ) =0 ,a 0 ,一致有界及全局渐近稳定的充分条件 .讨论一阶导数项 ax′( t-τ)对方程有界性及渐近稳定性的影响 .     

关于非线性微分方程一致渐近稳定性的扰动(Ⅱ)

<正> 本文用Ляпунов函数法从扰动的观点在Banach空间E中研究非线性微分方程 dx/dt=f(t,x) x(t_o)=x_o∈E(0≤t_o≤t<+∞)(1)和扰动系统 dy/dt=f(t,y)+g(t,y)y(t_o)=y_o∈E(0≤t_o≤t<+∞)(2)一致渐近稳定和全局一致渐近稳定的问题.     

关于双曲型偏微分方程u_xy=f(x,y,u,u_x,u_y)的唯一性问题

关于双曲型偏微分方程 u_(xy)=f(x,y,u,u_x,u_y),0≤x≤a,0≤y≤b,-∞相似文献   

求解对流扩散方程的紧致pade'逼近差分格式

将指数变换u(x,t)=p(x,t)e~(k/(2ε)x),p(x,t)=v(x,t)e~(st)、pade'逼近与紧致差分方法相结合,对线性对流扩散问题提出了精度为o(τ~4+h~4)的差分格式,分析了稳定性.最后通过数值算例说明格式的有效性.     

Global asymptotic stability of a class of nonautonomous integro-differential systems and applications

In this paper, we study the global asymptotic stability of a class of nonautonomous integro-differential systems. By constructing suitable Lyapunov functionals, we establish new and explicit criteria for the global asymptotic stability in the sense of Definition 2.1. In the autonomous case, we discuss the global asymptotic stability of a unique equilibrium of the system, and in the case of periodic system, we establish sufficient criteria for existence, uniqueness and global asymptotic stability of a periodic solution. Also explored are applications of our main results to some biological and neural network models. The examples show that our criteria are more general and easily applicable, and improve and generalize some existing results.     

Non-uniform asymptotic stability for the damped linear oscillator

Sufficient conditions are established for non-uniform asymptotic stability of a linear oscillator with damping term. The obtained results clarify a difference between the uniform asymptotic stability and the asymptotic stability. Some simple examples are included to illustrate the results. Especially, Bessel’s differential equations are taken up and it is proved that the equilibrium is asymptotically stable, but it is not uniformly asymptotically stable.     

$n$-维中立型多时滞微分方程的稳定性分析

This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The criterion on asymptotic stability is necessary and sufficient. Two examples are provided to illustrate the applications of our results. Some previous results are extended.     

变时滞随机模糊细胞神经网络稳定性分析(英文)

本文旨在研究一类带变时滞的随机模糊细胞神经网络的稳定性.通过构造恰当的Lyapunov泛函并运用线性矩阵不等式(LMI)理论,作者给出了保证这类神经网络全局渐近稳定的充分条件.本文推导出两个定理:一个用以判定文中模型的全局渐进稳定性,一个用以判定该模型在均方意义下的全局渐近稳定性.     

Weak asymptotic stability at first approximation for periodic differential inclusions

Weak asymptotic stability of an equilibrium position for a periodic differential inclusion is studied. First the weak asymptotic stability for a discrete-time inclusion generated by the original differential inclusion is investigated with the help of first approximation techniques. Then using the results for discrete-time inclusions the weak asymptotic stability for the differential inclusion is derived from the properties of its first approximation.     

Positivity and stability of linear functional differential equations with infinite delay

General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron‐Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stability of positive equations is presented. Furthermore, two sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, we applied the obtained results to problems of the exponential asymptotic stability of Volterra integrodifferential equations. To the best of our knowledge, most of the results of this paper are new.     

Stability of delayed cellular neural networks

Global asymptotic stability and exponential stability of delayed cellular neural networks is considered in this paper. Based on the Lyapunov stability theorem as well as a fact about the elemental inequality, some new sufficient conditions are given for global asymptotic stability and exponential stability of delayed cellular neural networks. The results are less conservative than those established in the earlier references. Three examples are given to illustrate the applicability of these conditions.     

Global asymptotic stability analysis for integro-differential systems modeling neural networks with delays

In this paper, the global asymptotic stability of the equilibrium point of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global asymptotic stability. The results have shown to improve the previous global asymptotic stability results derived in the literature. Some examples are given to illustrate the correctness of our results.     

Asymptotic Stability of Nonlinear Stochastic Evolution Equations

Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. Special attention is paid in proving sufficient conditions ensuring almost sure asymptotic stability with a non-exponential decay rate. The situation containing some hereditary characteristics is also treated. The results are illustrated with several examples.     

The analytic and numerical stability of stiff impulsive differential equations in Banach space

In this paper, we first introduce the test problem classes with respect to the initial value problems of nonlinear stiff impulsive differential equations in Banach spaces. The stability and asymptotic stability results of the analytic solution of the above-mentioned problems are obtained. As an example of discretization methods, the numerical stability and asymptotic stability results of the implicit Euler method are also given.