Stability results of random impulsive semilinear differential equations

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.     

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。     

隐稳定的充分条件

本文分析隐稳定矩阵的充分条件，得到几个关于低阶隐稳定矩阵扩充高阶后仍保持隐稳定的结果．     

Robust Stability of Positive Linear Systems Under Time-Varying Perturbations

By a novel approach, we get explicit robust stability bounds for positive linear differential systems subject to time-varying multi-perturbations and time-varying affine perturbations. Our approach is based on the celebrated Perron-Frobenius theorem and ideas of the comparison principle. An example is given to illustrate the obtained results.     

抛物化稳定性方程在可压缩边界层中应用的检验

用抛物化稳定性方程（PSE）,研究了可压缩边界层中扰动的演化,并与由直接数值模拟（DNS）所得进行比较．目的在检验PSE方法用于研究可压缩边界层中扰动演化的可靠性．结果显示,无论是亚音速还是超音速边界层,由PSE方法和由DNS方法所得结果都基本一致,而温度比速度吻合得更好．对超音速边界层,还计算了小扰动的中性曲线．与线性稳定性理论（LST）的结果相比,二者的关系和不可压边界层的情况相似．     

单种群离散模型的全局和局部稳定性

本文概述了关于单种群离散模型稳定性研究的成果,在此基础上,给出一些新的结果.     

脉冲微分方程的两度量实用稳定性

利用向量Lyapunov函数,研究了脉冲微分方程的两度量实用稳定性问题,通过实例对得到的稳定性的结论给予了验证.     

THE STABILITY OF A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

1 IntroductionConsider the following functional differential equationX'(t) = A(t)x(t) [' C(t,s)x(s)ds, (1)icwhere x E m; A(t) = (ail(t))... is a n x n function matrix, which continuesin [0, co); C(t,s) = (qj(t,8))... is a n x n function matrix, which conti-nues when 0 5 s 5 t < co, and L oo IIC(u,t)lldu continues in [0, co).The problem on the stability for the zero solution of (1) has been studied bymany papers. But in the known results, the boundedness of j: IIC(t, s)lldsor L " IIC…     

纬向对称准地转流的非线性稳定性定理

建立了周期域上准地转流在一般的边界条件下对应于Arnold第二定理的非线性稳定性定理。将扰动能量与扰动拟能的上界用初始扰动场的显示表示出来，从而建立了Liapunov意义下的非线性稳定性定理。     

Volterra系统全局稳定、扇形稳定及关联稳定的一些新判据

Stability of Volterra systems are discusses by subpositive definite matrix, and some new criterions for Volterra systems on overall situation stability, sector stability and connection stability are acquired. These results expand or improve some existing criterions.     

Lurie不确定间接控制系统的鲁棒绝对稳定性

利用Razumikhin技术和向量不等式方法,通过构造适当的Lyapunov函数,对具有多个时变时滞lurie不确定间接控制系统的鲁棒绝对稳定性的问题进行了研究,给出了该系统时滞相关鲁棒稳定的充分条件.其结论与已有文献结果进行比较,说明所得结果推广了已有文献的结果,具有更好的实用性.最后给出一个例子说明本文结果.     

某类系统广义指数型E稳定性(英文)

研究某类系统广义指数型 E稳定性 ,推广了文献 [1 ],[2 ]的某些结果 .     

含两组状态变量且参数具有对称性的等变分歧问题及其开折的稳定性

基于奇点理论中光滑映射芽的接触等价关系,讨论含两组状态变量且分歧参数带有对称性的等变分歧问题及其开折的稳定性,得到了一些基本结果,并且用横截性条件刻划了等变分歧问题的稳定性．     

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.     

■混合序列加权和的强稳定性(英文)

本文给出了■混合序列加权和的强稳定性的一些结果,同时也给出了■混合序列的强大数定律的若干新结果,这些结果推广了独立随机变量序列的相应结果.     

非线性系统稳定分析的特征函数法及其应用

本文引入一个特征函数,用于定量刻画非线性常微分方程的指数稳定性。与常用的Lyapunov方法相比,该方法简单、易用、而且易获得对一族范数（所有单调范数）皆成立的稳定性条件。所获结果推广了稳定理论中的一些著名结论,并应用于非线性连续神经网络的指数稳定性分析,推广和深化了[1-3]所获得的基本结论。     

Study of a fractional-order model of chronic wasting disease

This paper studies a fractional-order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non-negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf-type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained.     

基于一类积分不等式上的中立型时滞微分方程的稳定性

利用一类积分不等式以及参数变易法,Jensen不等式,给出了更为一般的中立型时滞微分系统的Lyapunov稳定性的判别准则,推广和改进了一些文献中有关中立型微分方程的Lyapunov稳定性的结论.     

Stability for systems of 1-D coupled nonlinear oscillators

The stability of the null solution of different systems of differential equations describing the motion of 1-D coupled nonlinear oscillators is discussed. Under certain assumptions we derive some stability results. Specifically, in the case of coupled damped oscillators we obtain asymptotic stability of the null solution (see Theorem 3.1, Example 3.1, and Fig. 2), while in the case of partial lack of damping we only obtain convergence to zero of the solution components corresponding to damped oscillators (see Theorem 4.1, Example 4.1, and Fig. 5). In all cases, including the case of coupled undamped oscillators, we obtain uniform stability of the null solution.     

学习算法的稳定性与泛化(Ⅱ):有界差分稳定框架

根据有界差分条件,提出了学习算法的有界差分稳定框架.依据新框架,研究了机器学习阈值选择算法,再生核Hilbert空间中的正则化学习算法,Ranking学习算法和Bagging算法,证明了对应学习算法的有界差分稳定性.所获结果断言了这些算法均具有有界差分稳定性,从而为这些算法的应用奠定了理论基础.