基于亚正定阵的Volterra系统稳定性的若干新判据

将亚正定阵引入到V o lterra系统,获得了判定该系统在正的平衡态全局稳定、扇形稳定及关联稳定的另一些新方法.从应用情况看,本文方法是有效的而且更为实用.     

非线性中立型延迟微分方程单支方法的数值稳定性

本文研究Rα,β类非线性中立型延迟微分方程单支方法的数值稳定性,结果表明:A-稳定的单支方法是数值稳定的,强A-稳定的单支方法是渐近稳定的．最后的数值试验验证了所获理论结果的正确性．     

非线性中立型延迟积分微分方程Runge-Kutta方法的稳定性

获得了求解非线性中立型延迟积分微分方程的Runge-Kutta方法稳定及渐近稳定的条件,数值实验结果验证了所获理论的正确性.     

泛函微分方程的弱指数渐近稳定性

本文提出一种新的稳定性概念,即弱指数渐近稳定,并给出两个关于弱指数渐近稳定的判别定理和一个较广泛的指数渐近稳定判别结果.从而使得许多具有一致渐近稳定性的解的趋零速度,得到了一种估计.文中还深入地揭露了一致渐近稳定性和弱指数渐近稳定性之间的内在联系以及弱指数渐近稳定性和指数渐近稳定性的关系.     

渐近平均稳定信道的各态历经性

本文讨论了渐近平均稳定信道的各态历经性,尤其是证明了v_x,v_x文于ams信道[A, v, B]的拟各态历经性以及v的稳定平均的v,得到了渐近平均稳定信道为各态历经的一个充分必要条件。     

滞后型分段连续随机微分方程的稳定性

本文研究了滞后型分段连续随机微分方程的解析稳定性和数值稳定性问题.首先,利用伊藤公式等方法获得了解析解均方稳定的条件,其次,对于包括均方稳定和T-稳定在内的Euler-Maruyama方法的数值稳定性问题,运用不等式技术和随机分析方法获得了一些新的结果,证明了在一定条件下,Euler-Maruyama方法既是均方稳定又是T-稳定的,推广了随机延迟微分方程的数值稳定性结论.     

一个具有年龄结构非自治种群模型的稳定性与周期解

本文讨论一个具有年龄结构的非线性非自治种群模型解的渐近性态,得到了零解稳定和全局稳定的充分条件,也给出了周期解存在及稳定的判别准则。     

非线性中立型延迟积分微分方程单支方法的稳定性分析

本文研究求解R(α,β1,β2,γ)类非线性中立型延迟积分微分方程单支方法的数值稳定性,结果表明:在一定条件下,A-稳定的单支方法是数值稳定的,强A-稳定的单支方法是渐近稳定的,最后的数值试验验证了所获理论的正确性.     

论Лурье间接控制系统绝对稳定的充要条件

本文通过拓扑变换,将间接控制系统化为变量分离的非线性控制系统,引进部分变元绝对稳定的概念,得到绝对稳定的充要条件,理论上解决了悬而未决的问题,然后给出一系列新的实用的充分条件。     

求解广义中立型系统的线性多步方法的NGP_G-稳定性

建立了广义中立型延迟系统理论解渐近稳定的充分条件 ,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性 ,在一定的Lagrange插值条件下 ,证明了数值求解广义中立型系统的线性多步方法NGPG_稳定的充分必要条件是线性多步方法是A_稳定的·     

关于运用Liapunov函数的滞后型系统部分稳定性的注释

Sufficient conditions for the stability with respect to part of the functional differential equation variables are given. These conditions utilize Lyapunov functions to determine the uniform stability and uniform asymptotic stability of functional differential equations. These conditions for the partial stability develop the Razumikhin theorems on uniform stability and uniform asymptotic stability of functional differential equations. An example is presented which demonstrates these results and gives insight into the new stability conditions.     

二元稳定网络的算法及模型

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.     

差分方程解的稳定性、有界性及概周期解的存在性

作者通过Liapunov泛函建立了一类高维差分方程解一致稳定、一致渐近稳定及指数渐近稳定的充要条件. 此外, 作者还证明了解的一致渐近稳定性蕴含解的有界性, 同时也给出了概周期差分方程存在概周期解的一个充分条件.     

Mittag-Leffler-Ulam stabilities of fractional evolution equations

In this paper, we present and discuss four types of Mittag-Leffler-Ulam stability: Mittag-Leffler-Ulam-Hyers stability, generalized Mittag-Leffler-Ulam-Hyers stability, Mittag-Leffler-Ulam-Hyers-Rassias stability and generalized Mittag-Leffler-Ulam-Hyers-Rassias stability for a fractional evolution equation in Banach spaces.     

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

Stability of functional equations in single variable

This paper discusses Hyers-Ulam stability for functional equations in single variable, including the forms of linear functional equation, nonlinear functional equation and iterative equation. Surveying many known and related results, we clarify the relations between Hyers-Ulam stability and other senses of stability such as iterative stability, continuous dependence and robust stability, which are used for functional equations. Applying results of nonlinear functional equations we give the Hyers-Ulam stability of Böttcher's equation. We also prove a general result of Hyers-Ulam stability for iterative equations.     

Stable exact solutions in cosmological models with two scalar fields

We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.     

一类不确定时滞系统的鲁棒稳定性

给出了不确定时滞系统鲁棒稳定的若干结果,同时讨论了这类系统的稳定度,改进了前人关于时滞系统稳定性和鲁棒稳定性的一些结论,并给出了应用的例子。     

Exponential stability for set dynamic equations on time scales

A new theory known as set dynamic equations on time scales has been built. The criteria for the equistability, equiasymptotic stability, uniform and uniformly asymptotic stability were developed in Hong (2010) [1]. In this paper, we consider the exponential stability, exponentially asymptotic stability, uniform and uniformly exponentially asymptotic stability for the trivial solution of set dynamic equations on time scales by using Lyapunov-like functions.     

金融机构的稳定性

用系统的观点分析金融稳定性问题,先简介了金融系统的有关概念,比较了金融稳定性和生态学稳定性概念以及金融生态环境与金融系统稳定性的关系,讨论了与金融稳定性有关的问题,论证了金融机构确定模型和随机模型以及具有下临界点L的金融机构模型的稳定性,构建并论述了金融群落、金融群落层级结构系统的稳定性.