Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

一类具脉冲干扰的Cohen—Grossberg时滞神经网络模型的全局指数稳定性

本文主要考虑了一类带脉冲的Cohen—Grossberg时滞神经网络模型的全局指数稳定性，通过构造Liapunov函数，应用M矩阵理论和一些不等式的技巧，给出了模型的平凡解全局指数稳定的充分条件。     

Global exponential stability of impulsive integro-differential equation

In this paper, an impulsive integro-differential equation is considered. By establishing an integro-differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, some new sufficient conditions for global exponential stability of impulsive integro-differential equation are obtained. The results extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the theory.     

Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen-Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.     

随机脉冲微分系统指数稳定性

该文首先给出了具有随机脉冲时刻影响的非线性微分系统 模型，然后得到了该模型零解的p阶矩指数稳定和几乎必然指数稳定的充分条件，在所得结果中不要求dV(t,x(t)) /dt定负．最后，给出一个例子说明所得结果的应用．     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS

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Stability analysis of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms

In this paper, we investigate a class of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. By establishing an integro-differential inequality with impulsive initial conditions and applying M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness, global exponential stability and global robust exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. An example is given to illustrate the results obtained here.     

Impulsive control for differential systems with delay

This paper deals with the impulsive control for a class of differential systems with delay. Using Lyapunov functions and the comparison principle, we present some sufficient conditions for the asymptotic stability and exponential stability of impulsive control systems with delay. Moreover, we give an estimate of the upper bound of impulse interval. The results in this paper extend and improve the earlier publications. Copyright © 2012 John Wiley & Sons, Ltd.     

含混合时滞和脉冲的Cohen-Grossberg神经网络的全局指数稳定性

本文讨论了含混合时滞和脉冲的Cohen-Grossberg神经网络的稳定性.通过应用M矩阵理论和不等式技巧,得到了含混合时滞的Cohen-Grossberg神经网络平衡态的全局指数稳定性的充分条件.相比以前同类文献,本文减弱了部分条件,推广了部分结论,并在文末给出了两个示例.本文结论对于设计和应用神经网络有一定实用价值.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

变时滞的退化滞后型微分系统的稳定性

主要研究了具有变时滞的退化时滞微分系统的稳定性.利用退化时滞微分系统的变易公式和Gronwall-Bellman积分不等式给出了该系统的指数估计以及稳定和指数渐近稳定的充分条件.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

Stability of nonlinear variable-time impulsive differential systems with delayed impulses

This paper investigates the stability of nonlinear variable-time impulsive differential systems with delayed impulses. By using the comparison principle, the Lyapunov method and inequality techniques, some sufficient conditions for quasi-uniformly asymptotic stability and quasi-exponential stability of a given solution of variable-time impulsive differential systems with delayed impulses are established.     

具有时滞的抑制细胞神经网络的周期解的存在性和全局指数稳定性

By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.     

具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性

本文讨论了具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性.通过建立一个脉冲时滞%积分微分不等式,以及模糊逻辑算子与M-矩阵的性质,不仅得到了系统全局指数稳定的充分条件,而且也给出了指数收敛速度.最后,所给的例子充分验证了文中所给出的充分条件的有效性.     

变时滞Hopfield神经网络的周期解存在性及其全局指数稳定性

利用拓扑度理论中的连续性引理和推广Halanay不等式研究了变时滞的细胞神经网络的周期解的存在性及全局指数稳定性.给出了判别周期解及指数稳定性的代数判据,所得判据易于检验,具有广泛的实用性．同时,改进了已有文献的相关结论,最后通过数值例子说明结论的有效性．     

一类具分布时滞的Hopfield网络模型的概周期解存在性与稳定性

利用Banach空间压缩不动点定理和微分不等式的分析技巧,研究一类具分布时滞的Hopfield神经网络模型的概周期解的存在性和稳定性。得到了系统存在概周期和全局指数稳定的新的充分条件。所得结果改进和推广了相关文献的结论。     

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

In this paper, we aim to investigate the exponential stability of general hybrid stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient to be applied than those Razumikhin‐type conditions in the literature. Meanwhile, we show that unstable hybrid stochastic delay differential systems, both linear and nonlinear, can be stabilized by suitably impulsive sequence. Finally, two examples are discussed to illustrate the effectiveness and advantages of the obtained results. Copyright © 2017 John Wiley & Sons, Ltd.     

EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

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时滞BAM神经网络周期解的存在性和全局指数稳定性

本文利用迭合度理论,通过构造适当的Lyapunov泛函并结合Yang不等式分析技巧,获得了具周期系数的时滞BAM神经网络周期解的存在性和全局指数稳定性的充分条件,这些结果对设计全局指数稳定的BAM神经网络与周期振荡的BAM神经网络具有重要的指导意义.