神经元传输函数对人工神经网络动力学特性的影响

以神经元局域场分布为基础，重新研究了连续神经元传输函数对具有联想记忆的人工神经网络功能的影响.与以往的认识不同的是，研究发现连续传输函数与硬极限传输函数相比并不存在明显的优越性，相反，连续传输函数对网络的某些功能，如最大存储率具有负面影响.研究表明神经网络的特性主要决定于网络的动力学结构(具体体现为网络吸引子对应的神经元局域场分布)，网络的动力学结构可以通过选择合适的设计规则进行有效控制，不同的传输函数虽然也能影响到网络的动力学结构，但是它所带来的影响是被动的，可控性很差. 关键词： 联想记忆 神经网络 吸引子 局域场分布     

Pair-correlated patterns in Hopfield model of neural networks

We study the retrieval properties of the Hopfield model of neural networks when the memorized patterns are statistically correlated in pairs. There is a finite correlationk between the memories of each pair, but memories of different pairs are uncorrelated. The analysis is restricted to the case of an arbitrary but finite number of memories in the thermodynamic limit. We find that there are two retrieval regimes: for 0<T<(1–k) the system recognizes the stored patterns and for (1–k)<T<(1+k) the system is able to recognize pairs, but it is not able to distinguish between its two patterns.     

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's functional and use of Finsler's lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.     

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.     

时滞双向联想记忆神经网络的全局稳定性

通过构造一个合适的Lyapunov泛函及应用不等式的分析技巧研究了具有时滞的双向联想记忆 神经网络的平衡点的全局稳定性问题-在对神经元激励函数较宽松的假设条件下（可以不满 足Lipschitz条件），获得了一个新的保证全局渐近稳定性的判定准则-结果可应用于包含非 Lipschitz的一类更加广泛的神经元激励函数的神经网络的设计中- 关键词： Lyapunov泛函 时滞 双向联想记忆神经网络 全局渐近稳定性     

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler’s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.     

Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties

This Letter deals with the problem of exponential stability for a class of delayed Hopfield neural networks. Based on augmented parameter-dependent Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stability are obtained for two cases of time-varying delays: the delays are differentiable and have an upper bound of the delay-derivatives, and the delays are bounded but not necessary to be differentiable. The conditions are presented in terms of linear matrix inequalities, which allow to compute simultaneously two bounds that characterize the exponential stability rate of the solution. Numerical examples are included to illustrate the effectiveness of our results.     

Theoretical analysis and computer simulations of the second-order Hopfield model

Theoretical analyses of the second-order Hopfield model show that the second-order Hopfield model with the bipolar binary (-1,1) vectors will have better than the samemodel with the unipolar binary (0,1) vectors.Computer simulations given in this paper con-firm this conclusion.     

A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional (3D) autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.     

Stochastic resonance in Hopfield neural networks for transmitting binary signals

We investigate the stochastic resonance phenomenon in a discrete Hopfield neural network for transmitting binary amplitude modulated signals, wherein the binary information is represented by two stored patterns. Based on the potential energy function and the input binary signal amplitude, the observed stochastic resonance phenomena involve two general noise-improvement mechanisms. A suitable amount of added noise assists or accelerates the switch of the network state vectors to follow input binary signals more correctly, yielding a lower probability of error. Moreover, at a given added noise level, the probability of error can be further reduced by the increase of the number of neurons. When the binary signals are corrupted by external heavy-tailed noise, it is found that the Hopfield neural network with a large number of neurons can outperform the matched filter in the region of low input signal-to-noise ratios per bit.     

基于混沌神经网络的盲检测改进新算法

针对Hopfield神经网络的多起点问题,提出了一种新的基于混沌神经网络的盲信号检测算法,实现了二进制移相键控信号盲检测.据此进一步提出双sigmoid混沌神经网络模型,构造了新的能量函数,且证明了该模型的稳定性,并对网络参数进行配置.仿真实验表明:混沌神经网络能够避免局部极小点且具备较强的抗噪性能,双sigmoid混沌神经网络则继承了其所有的优点,且其收敛速度更快,仅需更短的接收数据即可到达全局真实平衡点,从而降低了算法的计算复杂度,减少了运行时间.     

Synthesization of high-capacity auto-associative memories using complex-valued neural networks

In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks.One numerical example is provided to show the effectiveness and superiority of the presented results.     

Dynamic behaviors of a class of memristor-based Hopfield networks

In this Letter, we analyze the dynamic behaviors for a class of memristor-based Hopfield networks. Some sufficient conditions are obtained which ensure the essential bound of solutions and global exponential stability of memristor-based Hopfield networks by using analysis approaches, and the criteria act as significant values for qualitative analysis of memristor-based Hopfield networks. Finally, a numerical example is given to show the effectiveness of our results.     

基于矢量量化及Hopfield模型的灰度级图像识别

提出了一种新的识别灰度级图像的方法，该方法基于矢量量化的基本思想，通过对图像的分割，将灰度级图像映射成神经元仅取少数和几种状态的Ｈｏｐｆｉｅｌｄ神经网络模型，理论和模拟实验证明：这种低状态的ｏｐｆｉｅｌｄ与传统灰度图像识别模型相比，不仅神经元的数目较少，互连密度较低，而且网络具有较好的联想能力。     

两维局域互联神经网络的关联存储

本文将局域互联神经网络的新概念推广到两维情形,并对两维局域互联关联存储进行了理论分析和大量的计算机模拟.结果表明,两维局域互联神经网络的优点是,在满足存储容量限制的前提下,它与全局互联神经网络具有相同的关联存储能力,而其互联权重矩阵要比全局互联网络小得多.因而,有利于使用现有的空间光调制器实现两维大规模的人工神经网络.     

正补态光学神经网络模型性能评估

本文对一种多值光学神经网络模型——正补态模型的性能,存贮容量、容错性及收敛性进行了评估,并在N=16的网络上进行了计算机模拟.结果表明,正补态模型的性能比其它光学神经网络模型有所改善.     

An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

In this study,a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional.This paper presents the comprehensive discussion of the approach and also extensive applications.     

Computer simulations of the first-order and secondorder heteroassociative interpattern association models and their applications for the heteroassociative loop

The heteroassociative interpattern association (IPA) model and the second-orderheteroassociative IPA model,developed from the IPA model are discussed in this paper.Andcomputer simulations of these models,in comparison with the corresponding-order heteroasso-ciative Hopfield models,are given.The heteroassociative IPA models for the heteroassociativeloop is also given.     

基于幅值相位型离散Hopfield神经网络的多进制振幅键控盲检测

针对统计量算法盲检测多进制振幅键控(MPSK)信号的缺陷, 提出了一种幅值相位型连续多值复数Hopfield神经网络算法, 构造了适用于MPSK信号的幅相型离散多电平激活函数,并分别在异步和同步更新模式下证明了该神经网的稳定性.当该神经网的权矩阵借助接收数据补投影算子构成时, 该幅相型离散Hopfield神经网络可有效地实现MPSK信号盲检测. 仿真试验表明:该算法所需接收数据较短,可到达全局真解点,并且适用于含公零点信道.