一类非线性时滞差分方程的稳定性

得到了一类线性非自治时滞差分方程的零解的一致稳定、一致渐近稳定和全局渐近稳定的充分条件.     

具斑块迁移的病毒模型的稳定性分析

研究了一类未感染细胞斑在两斑块间迁移的病毒模型.获得了无病平衡点全局稳定性以及地方病平衡点稳定性的充分条件.研究结果表明阈值R <1且感染细胞生成病毒的速度相对小而病毒细胞死亡率足够大时,病毒趋于灭绝;而阈值R> 1且感染细胞生成病毒的速度相对大而病毒细胞死亡率足够小时,病毒持续流行.     

一类具有两阶段结构的自治SIS传染病系统

讨论了具有两阶段结构的自治SIS传染病系统,证明了该系统的边界平衡态和正平衡态的全局渐近稳定性,得到了使其渐近稳定的阈值.     

有限时滞差分方程的稳定性

在本文中,作者建立了一些定理可以确保系统：x(n 1)=f(n,xn）（1）为一致稳定、渐近稳定或一致渐近稳定。在所获得的定理中,不要求△V为常负,这里△V（n,xn)≡V(n 1,x(n 1)-V(n,x(n))=V(n 1,f(n,xn)))-V(n,x(n)),特别地,在定理1中,△V甚至可以恒为正,这大大地改进了已有结果并且更加便于应用。     

关于扰动微分方程零解稳定性若干定理的改进

本文运用Ляиунов第二方法研究扰动微分方程零解稳定性，分别研讨了所给扰动微分方程的局部稳定性、全局渐近稳定性以及全局一致渐近稳定性问题，得到若干定理，这些结果在一定条件下改进了文[1]的相应结果，运用更加广泛．     

ON UNIFORM ASYMPTOTIC STABILITY OF INFINITE DELAY DIFFERENCE EQUATIONS

51. IntroductionThe aim of thi8 paPer is to establish the stability criteria for the indnite de1ay differenceequations of the formx(n 1) = F(n,x.) for n E Z, (1'l)where F: Z x CH -- Rk, Z denotes the integer set, Rh is the n-dimensional Euclidean space,CH = {T E C: llWII < H} fOr some constan H > 0, whileC = {yt: {... l --2, --1,0} - Rk l W is bounded}withllytIl = sup IW(8)I for W E C,8<0and x.(8) = x(n 8) for 8 5 0. Here, and in the sequel, l' I is a norm in Rk, and we atwa…     

On pathwise super-exponential decay rates of solutions of scalar nonlinear stochastic differential equations

This paper studies the pathwise asymptotic stability of the zero solution of scalar stochastic differential equation of Itô type. In particular, we provide conditions for solutions to converge to zero at a given rate, which is faster than any exponential rate of decay. The results completely classify the rates of decay of many parameterised families of stochastic differential equations.     

Guaranteed asymptotic stability for a class of uncertain linear dynamical systems

We consider a class of linear dynamical systems with bounded, Lebesgue-measurable uncertainties in the system and input matrices as well as in the input itself. A state feedback control is derived, which guarantees global, uniform asymptotic stability of the zero state; this control is continuous, except at the zero state.This paper is based in part on research supported by the National Science Foundation.     

非线性灰色离散系统零解的稳定性

本文用区间矩阵和Ｌｙａｐｕｎｏｖ第二方法讨论了具有非线性扰动项的灰色离散系统的稳定性，得到了若干稳定性的代数判据，这些结果将文（５）的主要结果由线性推广到了非线性，并给出了实现的例子。     

On the recursive sequence

Our aim in this paper is to investigate the global asymptotic stability of all positive solutions of the higher order nonlinear difference equation

where B, C and α, β, γ are positive, k {1, 2, 3, … }, and the initial conditions x_−2k+1, … , x₋₁, x₀ are positive real numbers. We show that the unique positive equilibrium of the equation is globally asymptotically stable and has some basins that depend on certain conditions posed on the coefficients. Our concentration is on invariant intervals, the character of semicycles, and the boundedness of the above mentioned equation. Our final comments are about informative examples.     

基于一类时滞不等式的时滞微分方程的渐近稳定性

利用Lyapunov的方法讨论了时滞微分方程x.(t)=f(t,x(t),x(t-τ(t)))的全局指数渐近稳定性和全局渐近稳定性.     

Description of stability for linear time-invariant systems based on the first curvature

This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system $\text{◂=▸}\dot{r}(t)=\text{◂⋅▸}Ar(t)$, (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that $\text{◂≠▸}\underset{t\to +\infty }{\lim }\kappa (t)\ne 0$ or $\underset{t\to +\infty }{\lim }\kappa (t)$ does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that $\text{◂=▸}\underset{t\to +\infty }{\lim }\kappa (t)=+\infty$ for any initial value in this set, then the zero solution of the system is asymptotically stable.     

具有桥梁人群的HIV模型的研究

研究了具有桥梁人群(从事性服务的女性静脉吸毒者)的艾滋病模型.在桥梁人群内部建立一个DI模型.通过定性分析,证明了各类平衡点的稳定性,从而判断艾滋病流行与否.     

具有桥梁人群的HIV模型的持续生存

给出了一致持续性的一些概念及基本理论,建立了具有桥梁人群的H IV模型.利用所给结论研究了具有桥梁人群的H IV模型的一致持续性,从而说明艾滋病会流行起来.     

稳定性切换在一阶时滞微分方程中的应用

介绍了时滞动力系统中的对零解稳定性讨论的稳定性切换法,并应用此方法对时滞动力系统中的三个一阶时滞微分方程基本定理给予证明.同时表明了在局部稳定性分析中,该方法有着更大的优势.     

STABILITY THEOREMS FOR IMPULSIVEDIFFERENTIAL SYSTEMS

1IlltroductionTherearealotofgoodresultsonthestudyofthestabilityofimpulsivedifferentialsystems.Thepresentpaperisdevotedtotheinvestigationofakindofnonlinearimpulsivedifferentialsystems.Theoremsobtainedhereareonthestabilityandunstabilityoftrivialsolution.Theconditionsofthesetheoremsareverysimple.Inaddition,therearesomeexamplesfortheuseofthesetheorems.Especially,intheseexamples,wecanseethateventhoughthetrivialsolutionofaclassicaldifferentialsystemwithoutimpulsesisunstable,itwillbecomestableifwead…     

数值求解延时微分方程的步长准则

１．引言 用一个数值方法求解下列延时微分方程：其中, ｆ： Ｒ × Ｃｄ × Ｃｄ → Ｃｄ为给定函数, Ｕ（ｔ）当上＞ ０时为未知函数,τ＞ ０为常数延时量,ф（ｔ）∈Ｃｄ为已知向量值函数．为了检验一个数值方法的数值稳定性,常用如下试验方程：来观察方法的数值稳定性,这里ａ,ｂ∈Ｃ（Ｃ为复数集）为已知常数,ф（ｔ）为给定的连续函数（ｔ≤０）． 定义 １［2］．延时微分方程（简记为ＤＤＥＳ）（３）被称为是渐近稳定的,如果（３）的每一个解Ｕ（ｔ）满足 方程(３)的特征方程为： 定义 ２［２］．一数值方法求解ＤＤＥＳ称为…     

二阶非线性微分方程零解的全局渐近稳定性

本文研究了具有四个非线性项零解的全局渐近稳定性。