ON GLOBAL ROBUST STABILITY FOR INTERVAL HOPFIELD NEURAL NETWORKS WITH TIME DELAY

The theorem obtained by Liao was not true (see [2]). So, this paper presents some criteria of global robust stability for interval Hopfield neural networks with time delay. The methods to judge the robust stability are practical and easily verifiable.     

变时滞Hopfield神经网络的全局指数稳定性

本文研究了一类具有变时滞Hopfield神经网络的稳定性问题.利用时滞微分不等式方法,获得了几个关于该网络的全局指数稳定性与时滞无关的充分条件,并且给出了此类网络的收敛指数的估计,推广了已知文献的结果.最后给出数值例子证明结论的有效性.     

ON GLOBAL ROBUST STABILITY FOR COMPETITIVE NEURAL NETWORKS WITH TIME DELAYS AND DIFFERENT TIME SCALES

In this paper, using the theory of topological degree and Liapunov functional methods, the authors study the competitive neural networks with time delays and different time scales and present some criteria of global robust stability for this neural network model.     

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 DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH DELAYS

In this paper, a new sufficient condition for the global exponential stability of a unique equilibrium point of discrete-time cellular neural networks is given. It is shown that the condition relies on the feedback matrices and is independent of the delay parameter. Furthermore, this condition is less restrictive than those given in the literature.     

PERIODIC SOLUTIONS TO FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS

In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our resu...     

GLOBAL EXPONENTIAL STABILITY IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.     

GLOBAL ATTRACTIVITY OF THE HOPFIELD NEURAL NETWORKS

1 IntroductionHopfield neural networks is an associative memory model, it is also a neuraloptimization networks. This model has been studied extensively (see [1--12]).But in most of the literature, the signal function gi(x) is differentiable and isa sigmoid curve, and the sufficient conditions about the global attractivity ofthe Hopfield neural networks have no relevance to the delay. The aim of thispaper is to give a delayed sufficient condition of the global attractivity of theHopfield neur…     

GLOBAL ATTRACTIVITY IN DELAYED HOPFIELD NEURAL NETWORK MODEL WITH VARIABLE COEFFICIENTS AND DELAYS

1 Introduction' In paper [1], Hopfield first proposed neural network model for n neurons;with an electrical circuit implementation. Even since, there has been increasing interest in the potential application of the dynamics of artificial neuralnetworks in signal and image processing, see, for example, [2]--[5], they havestudied system (1.1) and the delayed systemwhere all ci ) Ri, Ti j ? h, T are constants.The global attractivity of system (1.l) or (1.2) is of great importance forboth practi…     

SCALE-TYPE STABILITY FOR NEURAL NETWORKS WITH UNBOUNDED TIME-VARYING DELAYS

This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks.     

变时滞细胞神经网络的指数稳定的一个充分条件

本文我们研究了变时滞细胞神经网络的指数稳定性。利用分析技巧，获得了变时滞细胞神经网络的指数稳定的充分条件，改进了已有文献中的相应结果。     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

STABILITY OF DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

In this paper, we study the existence and stability of an equilibrium of discrete-time Cohen-Grossberg BAM Neural Networks with delays. We obtain several sufficient conditions ensuring the existence and stability of an equilibrium of such systems, using discrete Halanay-type inequality and vector Lyapunov methods. In addition, we show that the proposed sufficient condition is independent of the delay parameter. An example is given to demonstrate the effectiveness of the results obtained.     

具有分布时滞耦合神经网络模型的全局同步性分析

本文研究了具分布时滞的神经网络的全局同步性.通过应用Lyapunov泛函和线性矩阵不等式,获得了关于模型全局同步性的几个判定准则,并通过对相关例子进行了数值的仿真,模拟结果与理论分析吻合.     

EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS AND VARIABLE COEFFICIENTS

In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system is studied. By using the Schauder's fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.     

具变时滞的细胞神经网络的周期解

本文研究了一类具变时滞细胞神经网络系统,利用重合度理论中的延拓定理、不等式的分析原理、矩阵理论和Lyapunov泛函方法,得到了该系统周期解的存在唯一性及全局指数稳定性的结论,不仅在一些应用领域上是可行的且易检验,而且为神经网络系统周期解的存在性论证,提供了一个新的有效方法.     

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.     

ASYMPTOTIC STABILITY OF A SINGULAR SYSTEM WITH DISTRIBUTED DELAYS

Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.     

EXPONENTIAL STABILITY AND PERIODIC SOLUTION OF HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.     

GLOBALLY ASYMPTOTIC STABILITY OF MULTI-DELAYED NEURAL NETWORKS

A sufficient condition is presented for the uniqueness and globally asymptotic stability of a class of neural networks with multiple time-varying delays. The result is less conservative than some recent results in the literatures.