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.     

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.     

一类非定常经济系统的Lyapunov稳定性

讨论了一类非定常经济系统的Lyapunov稳定性,给出了经济系统稳定和渐进稳定的充分条件和稳定的必要条件,同时得到与系统稳定性有关的临界积累率的解析表达式.结果可为经济政策的制定提供理论依据.     

分支问题开折的强（r|s）稳定性与弱（r|s）稳定性

该文讨论了分支问题开折的强（r,s）稳定性及弱（r,s）稳定性,并给出了（r,s）无穷小稳定性、强（r,s）稳定性及弱（r,s）稳定性的等价性．     

Stability analysis of uncertain fuzzy Hopfield neural networks with time delays

In this paper, the global stability problem of uncertain Takagi–Sugeno (T–S) fuzzy Hopfield neural networks with time delays (TSFHNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSFHNNs. Here, we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized stability region. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The proposed stability conditions are demonstrated with four numerical examples. Comparison with other stability conditions in the literature shows our conditions are the more powerful ones to guarantee the widest stability region.     

电力市场实用稳定性的判定条件

首次把实用稳定性的理论用于电力市场稳定性的研究中.结合Alvarado提出的电力市场动态模型,利用微分代数方程与特征值技术,从理论上研究电力市场的实用稳定性,并且给出了判断电力市场实用稳定、一致实用稳定和实用渐近稳定性的充分条件.利用这些实用稳定性条件,对于Alvarado给出的数值算例,可方便地利用初始数据判断电力市场模型的实用稳定性,并通过实例提供了假设模型中某个参数在电力市场变化中起主要作用,如何控制电力市场模型实用稳定性的方法.最后利用Maple软件包给出了参数变化引起模型实用稳定和不稳定的图形演示.     

Comparison of theories for stability of truss structures. Part 2: Computation of critical solution of stability

Critical solution of stability is the optimum solution of cross-sectional area with stability constraint. By applying the linear Eulerian theory of stability, the critical solution with discrete variables for general truss structures is computed in this paper. Then, in order to compare the results with the ones in previous publications and to reveal the applicability of various theories of stability, the critical solutions with continuous cross-sectional areas are computed for several examples by applying various theories of stability.     

$n$-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.     

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.     

Stability analysis of differential equations with maximum

In this paper, we investigate stability of the zero solution of differential equations with maximum by using Lyapunov functions and Razumikhin techniques. Sufficient conditions for stability, uniform stability and asymptotic stability of the zero solution of such equations are found.     

Total stability of perturbed systems of differential equations

The notion of Lipschitz stability for systems of ordinary differential equations (ODE) was introduced. In this paper, we will extend the total stability notion to a new type of stability called total Lipschitz stability. Some criteria and results are given. Our technique depends on Liapunov's direct method.     

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.     

Stability of equilibria of discrete-time systems in terms of invariant sets

We suggest a new approach to the verification of the stability (or asymptotic stability) of the equilibria of time-invariant discrete-time systems based on stability and asymptotic stability criteria stated in terms of invariant sets. A set-theoretic method for the verification of the conditions in these criteria is presented.     

Strict stability of impulsive functional differential equations

Strict stability is the kind of stability that can give us some information about the rate of decay of the solutions. There are some results about strict stability of differential equations. In the present paper, we shall extend the strict stability to impulsive functional differential equations. By using Lyapunov functions and Razumikhin technique, we shall get some criteria for the strict stability of impulsive functional differential equations, and we can see that impulses do contribute to the system's strict stability behavior.     

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.     

Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays

This paper is concerned with the study of the stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays. We are interested in the comparison between the analytical and numerical stability regions. First, we focus on scalar equations with real coefficients. It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution. Then, we consider the multidimensional case. A new stability condition for the stability of the analytical solution is given. Under this condition, the asymptotic stability of Gauss-Pouzet methods is investigated.      

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.     

Stability of Local Efficiency in Multiobjective Optimization

Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions.     

Uniform stability of switched nonlinear systems

In this paper, we investigate the stability properties of a general class of nonautonomous switched nonlinear systems. Sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are derived via multiple Lyapunov functions. Our results provide stability criteria for switched systems with both stable and unstable subsystems. Particularly, our results include some existing results as special cases or improve those in the literature. Several numerical examples are worked out to illustrate our results.