二阶神经网络的全局指数稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间,二阶神经网络较一般神经网络具有更快的收敛速度,对于二阶连续型Hopfield神经网络,用Lyapunov方法讨论平衡点的全局指数稳定性,给出了平衡点全局指数稳定的几个判别准则,作为特例,获得了连续型Hopfield神经网络全局指数稳定的新判据。     

Global exponential stability of impulsive high-order Hopfield type neural networks with delays

In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results.     

离散时间反馈神经网络的渐近行为研究

Hopfield神经网络是一类应用非常成功的人工神经网络模型，它是研究这个反馈神经网络的基础．该文主要研究离散时间、连续状态的反馈神经网络，它是Hopfield神经网络的推广．众所周知，研究反馈神经网络的稳定性不仅被认为是神经网络最基本、最主要的问题之一，同时也是神经网络各种应用的基础．文中主要研究离散时间反馈神经网络的稳定性，给出了连接权矩阵非对称的并且输入-输出函数是一般的S-函数的新的渐近收敛性条件及相应的收敛性结论．所获结果不仅推广了一些已有的结论，而且为反馈神经网络的应用提供了一定的理论基础．     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络 模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳 定性进行了新的分析.证明了神经网络连接权矩阵在给定的约束条件下有唯一的而且是渐近 稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳 定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经 网络.所做的分析扩展了以前的稳定性结果.     

Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays

In this paper, a class of high-order Hopfield neural networks with neutral distributed delays is considered. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of weighted pseudo-almost automorphic solutions for this class of networks by employing the Banach fixed-point theorem and differential inequality techniques. The results of this paper are completely new. An example is given to show the effectiveness of the proposed method and results.

     

Improved conditions for global exponential stability of recurrent neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.     

Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays

The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.     

Global exponential stability of a class of Hopfield neural networks with delays

This paper investigates global exponential stability of a class of Hopfield neural networks with delays based on contraction mapping principle, Lyapunov function and inequality technique. Some sufficient conditions are derived that ensure the existence, uniqueness, global exponential stability of equilibrium point of the neural networks. Finally, an illustrative numerical example is given to demonstrate the effectiveness of our results.     

Nonlinear measures: a new approach to exponential stabilityanalysis for Hopfield-type neural networks

In this paper, a new concept called nonlinear measure is introduced to quantify stability of nonlinear systems in the way similar to the matrix measure for stability of linear systems. Based on the new concept, a novel approach for stability analysis of neural networks is developed. With this approach, a series of new sufficient conditions for global and local exponential stability of Hopfield type neural networks is presented, which generalizes those existing results. By means of the introduced nonlinear measure, the exponential convergence rate of the neural networks to stable equilibrium point is estimated, and, for local stability, the attraction region of the stable equilibrium point is characterized. The developed approach can be generalized to stability analysis of other general nonlinear systems.     

Almost Periodic Solutions for SICNNs with Neutral Type Proportional Delays and <Emphasis Type="Italic">D</Emphasis> Operators

This article is concerned with shunting inhibitory cellular neural networks involving neutral type proportional delays and D operators. Applying Lyapunov functional method and differential inequality techniques, we employ a novel argument to establish some new criteria on the existence and generalized exponential stability of almost periodic solutions of the addressed systems. In addition, numerical simulations are carried out to verify our theoretical findings.     

一类具有时滞的广义Hopf ield 神经网络的全局稳定性

通过引入能量泛函，分析了一类具有时滞的广义Hopfield神经网络的全局稳定性．从理论上给出了该类网络为全局稳定的充分条件，证明了当时滞满足一个可计算的边界条件时，具有时滞的该类神经网络与相应的无时滞网络具有同样的全局稳定特性．仿真结果进一步证明了结论的有效性。     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Estimate of exponential convergence rate and exponential stabilityfor neural networks

Estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes Hopfield neural networks and cellular neural networks. Both local and global exponential convergence are discussed. Theorems for estimation of the exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction in the case of local exponential convergence are obtained. Simple conditions are presented for checking exponential stability of the neural networks.     

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

The global exponential stability problem is considered for a class of impulsive neural networks with piecewise constant arguments in this paper. By employing the Banach fixed point theorem and the Razumikhin-type technique, stability criterion is obtained for the existence, uniqueness and global exponential stability of the periodic solution. Typical numerical examples are given to illustrate the improvement in less conservatism of the results.     

一类具有变时滞的Hopfield型神经网络的全局指数稳定性

通过构造适当的Lyapunov函数,利用Halanay不等式和Young不等式,讨论一类具有变时滞的Hopfield型神经网络的全局指数稳定性.在对网络施加两个不同的神经元激励函数的条件下,导出网络全局指数稳定的一个充分条件,得到的充分条件在实际应用中易于验证,且有较小的保守性,因而对网络的应用和设计具有重要意义.最后,一个数值实例进一步验证结果的正确性.     

Design of Hopfield network for cryptographic application by spintronic memristors

Memory being one of the essential credential in today’s computer world seeks forward newer research interests in its types. Hopfield neural networks of artificial neural networks are one of its classes that can be modelled to form an associative memory. In this paper, we have shown the Hopfield neural network constructed with spintronic memristor bridges accounting to act as an associative memory unit. The memristors are nanoscaled, in terms of size, which possess synaptic behaviour in the artificial neuromorphic system. The associative behaviour is realised by the updation of synaptic weights of memristive Hopfield with single- and multiple-bit associativity which is simulated in MATLAB. The application of the hardware in the field of cryptography is also proposed.

     

Global Robust Exponential Stability of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the equilibrium point of interval neural networks with delays are obtained. The delayed Hopfield network, Bidirectional associative memory network and Cellular neural network are special cases of the network model considered in this Letter. This revised version was published online in June 2006 with corrections to the Cover Date.     

Almost periodic solutions for Hopfield neural networks with continuously distributed delays

In this paper Hopfield neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.     

多时滞Hopfield神经网络的鲁棒稳定性分析及吸引域的估计

The robust stability of a class of Hopfield neural networks with multiple delays and parameter perturbations is analyzed. The sufficient conditions for the global robust stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. The conditions take the form of linear matrix inequality (LMI), so they are computable and verifiable efficiently. Furthermore, all the results are obtained without assuming the differentiability and monotonicity of activation functions. From the viewpoint of system analysis, our results provide sufficient conditions for the global robust stability in a manner that they specify the size of perturbation that Hopfield neural networks can endure when the structure of the network is given. On the other hand, from the viewpoint of system synthesis, our results can answer how to choose the parameters of neural networks to endure a given perturbation.