具有脉冲的高阶时滞Hopfield神经网络的全局指数稳定性

高阶Hopfield神经网络可以看作是Hopfield神经网络的扩展,相对一阶神经网络而言,高阶神经网络在存储能力、逼近能力、容错水平和收敛速度等方面具有更强大的能力.利用构造合适的Lyapunov泛函,应用不等式性质,研究了一类具有脉冲的高阶时滞Hopfield神经网络的动力学行为,得到了确保该系统的平衡点全局指数稳定的充分判别条件.通过两个仿真例子,说明所得结论的有效性.     

带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性

讨论了带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性.通过构造合适的Lyapunov函数,获得了判定带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性的充分条件.     

BP模式识别与Hopfield联想记忆识别能力的比较

神经网络可以进行模式识别,这一功能具有很高的实用价值.主要研究BP神经网络和离散Hopfield神经网络的识别能力.BP网络是前向神经网络,使用的是监督式学习规则.离散Hopfield是一种反馈网络,结构上输入、输出节点相连使得网络系统的输出状态具有动态变化特性.就数字,字母,手写体数字比较了BP网络和离散Hopfield网络的识别能力,得到了可观的结论,对两个网络的应用做更进一步的阐述.     

时滞Hopfield神经网络模型渐进稳定性的新准则

在不考虑激励函数有界,可微和单调的情况下,利用Lyapunov泛函方法,得到了时滞Hopfield神经网络模型的平衡点存在性和全局渐近稳定性的新准则.研究结果改进和推广了以前相关文献的结果.     

具有混合时滞的中立型Hopfield神经网络的概周期解

研究一类具有混合时滞的中立型Hopfield神经网络概周期解.通过运用指数二分性及不动点定理,获得了其概周期解的存在性与全局指数稳定性的充分条件,所得结果是新的,并且推广和改进了已有文献的相关结果.     

具有变时滞Hopfield神经网络的概周期解存在性与全局吸引性

该文利用不动点理论和微分不等式分析等技巧，研究了变时滞Hopfield神经网络概周期解存在性及其全局吸引性, 所得准则改进了相关文献的结果。     

具有变时滞和脉冲效应的Hopfield神经网络的全局指数稳定性

讨论了一类具有变时滞和脉冲效应的Hopfield神经网络模型．利用按段连续的向量Liapunov思想方法,研究了脉冲时滞神经网络的全局指数稳定性．例子及其数值仿真说明了结果的有效性．推广和改进了已有文献的一些结果．     

变系数分布DCNNS的全局稳定性研究

基于全局Lipschitz连续激励函数方法探讨了带有时滞的变系数Hopfield神经网络模型,借助不动点和Lyapunov泛函数确保给定的神经网络的全局渐进稳定.     

Hopfield型神经网络的稳定性

本文给出了 Hopfield 型神经网络平衡态稳定性的一系列判别准则,讨论了其平衡态的存在唯一性.     

连续型BAM神经网络的指数稳定性

首先将连续型双向联想记忆神经网络转化成一个特殊的Hopfield网络模型.在此基础上,对连续BAM神经网络的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平衡点.所做的分析可以用于设计全局指数稳定的神经网络.     

神经网络平衡点存在唯一的充要条件

针对一类广泛的激活函数 ,利用矩阵理论 ,建立了相应的Hopfield神经网络平衡点存在唯一的充要条件 .同时 ,也给出相应的离散神经网络平衡点存在唯一的充要条件 .比较现有的文献 ,本文的结果适用范围更为广泛     

Stability analysis of fractional-order complex-valued neural networks with time delays

In this paper, we consider the problem of stability analysis of fractional-order complex-valued Hopfield neural networks with time delays, which have been extensively investigated. Moreover, the fractional-order complex-valued Hopfield neural networks with hub structure and time delays are studied, and two types of fractional-order complex-valued Hopfield neural networks with different ring structures and time delays are also discussed. Some sufficient conditions are derived by using stability theorem of linear fractional-order systems to ensure the stability of the considered systems with hub structure. In addition, some sufficient conditions for the stability of considered systems with different ring structures are also obtained. Finally, three numerical examples are given to illustrate the effectiveness of our theoretical results.     

Stationary oscillation for high-order Hopfield neural networks with time delays and impulses

We investigate stationary oscillation for high-order Hopfield neural networks with time delays and impulses. In a recent paper [J. Zhang, Z. J. Gui, Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays, Journal of Computational and Applied Mathematics 224 (2008) 602-613], the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for high-order Hopfield neural networks with time delays and impulses. In this paper, we point out that the main result of the recent paper is unture, and present a new sufficient condition of stationary oscillation for the neural networks. A numerical example is given to illustrate the effectiveness of the obtained result.     

具有跳跃的随机神经网络的均方稳定性

研究了一类新的具有脉冲跳跃的Hopfield神经网络系统模型,其中脉冲时刻的跳跃是由一般的随机序列所引起,通过运用Lyapunov函数方法,获取了一些新的均方稳定性结果.由于脉冲的跳跃使得不稳定的神经网络变成稳定,因而所得的结果也可以运用到其他相关领域.     

Horseshoe chaos in a class of simple Hopfield neural networks

A class of new simple Hopfield neural networks is revisited. To confirm the chaotic behavior in these Hopfield neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

The split-step θ-methods for stochastic delay Hopfield neural networks

In this paper, we construct a new split-step numerical method for stochastic delay Hopfield neural networks. The main aim of this paper is to investigate the mean-square stability of this split-step θ-methods for stochastic delay Hopfield neural networks. It is proved that the split-step θ-methods are mean-square stable under suitable conditions. Numerical experiments verify the numerical stability results obtained from theory. A comparison between this work and Ronghua et al. [8] is also discussed in the example.     

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…