非对称联接神经网络的稳定性和稳定控制

本文对连续竞争神经网络提出一种新的动态分析方法,得出一类联想网络稳定的必要条件。根据这一稳定性准则,给出了一类联想神经网络的综合方法。对于一般不稳定网络,提出了网络稳定控制的方法。这种方法也为稳定网络的动态控制和优化提供了一条新途径。     

STUDIES OF THE DYNAMIC BEHAVIORS OF A CLASS OF LEARNING ASSOCIATIVE NEURAL NETWORKS

This paper investigates exponential stability and trajectory bounds of motions of equilibria of a class of associative neural networks under structural variations as learning a new pattern. Some conditions for the possible maximum estimate of the domain of structural exponential stability are determined. The filtering ability of the associative neural networks contaminated by input noises is analyzed. Employing the obtained results as valuable guidelines, a systematic synthesis procedure for constructing a dynamical associative neural network that stores a given set of vectors as the stable equilibrium points as well as learns new patterns can be developed. Some new concepts defined here are expected to be the instruction for further studies of learning associative neural networks.     

Global exponential stability and periodicity of recurrent neural networks with time delays

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time delays, and are also shown to be different from and improve upon existing ones.     

一类学习联想神经网络的动态特性研究

本文讨论了一类联想神经网络在学习过程中结构变化引起网络平衡点状态变化的动态特性;研究了网络的指数稳定性质;分析了联想过程中输入激励在噪声干扰情况下,网络的滤波能力;得到了一些对于研究联想神经网络学习性质有用的结论。     

Hopfield型联想记忆神经网络一种新的分析方法

本文通过定义一种新的能量函数，分析了Ｈｏｐｆｉｅｌｄ型神经网络的渐近稳定性与联想记忆问题，得到了四组保证网络平衡点是渐近稳定平衡点的充分条件，应用这些条件，便可设计联想记忆神经网络，文中给出了应用这些结论设计联想记忆神经网络的实验结果及分析。     

连续神经网络学习过程的动态特性研究

本文研究了连续神经网络在学习过程中结构摄动情况下网络的动态特性.首先提出一般连续神经网络的时变非线性微分方程模型,给出了结构摄动情况下网络在平衡点处线性化处理方法.并主要针对联想神经网络,研究了网络结构不变情况下和网络结构有界缓变的动态特性.     

Delay-Dependent Exponential Stability Criterion for BAM Neural Networks with Time-Varying Delays

By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.     

Mathematical foundations of neurocomputing

An attempt is made to establish a mathematical theory that shows the intrinsic mechanisms, capabilities, and limitations of information processing by various architectures of neural networks. A method of statistically analyzing one-layer neural networks is given, covering the stability of associative mapping and mapping by totally random networks. A fundamental problem of statistical neurodynamics is considered in a way that is different from the spin-glass approach. A dynamic analysis of associative memory models and a general theory of neural learning, in which the learning potential function plays a role, are given. An advanced theory of learning and self-organization is proposed, covering backpropagation and its generalizations as well as the formation of topological maps and neural representations of information     

带阶梯输出函数的细胞神经网络

本文给出了带阶梯输出函数的细胞神经网络的稳定性定理。利用阶梯输出函数的各“台阶”记忆不同灰度，实现了灰度模式的ＣＮＮ联想记忆。     

STABILITY OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DELAYS

In this paper the globally asymptotic stability of more general two-layer nonlinear feedback associative memory neural networks with time delays is examined. The sufficient conditions of existence, uniqueness and globally asymptotic stability of the equilibrum position are given. Finally, two interesting examples to illustrate the theory are given.     

分形细胞神经网络用于联想记忆

本文提出了分形细胞神经网络，并成功地应用于联想记忆，从模拟结果看，分形细胞神经网络的联想记忆能力好于Ｂａｒａｍ提出的分形神经网络。     

QUALITATIVE ANALYSIS OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS

In this paper, the global exponential stability of an equilibrium position for general bidirectional associative memory neural networks are studied. The sufficient conditions of existence and uniqueness of the equilibrium position are given. The method of energy function is examined. Two examples are given to illustrate the theory.     

Global asymptotic stability of a class of feedback neural networks with an application to optimization problems

By applying results from homotopy theory, new conditions are obtained for the existence and uniqueness of an equilibrium for a class of continuous-time feedback neural networks which contains the Hopfield model as a special case. Next, new criteria are established for the global asymptotic stability of the unique equilibrium of this class of neural networks by utilizing Lur'e-type Lyapunov functions and the stability theory for systems of differential inequalities. Several practical stability testing conditions are given. As a special case, criteria are derived for the global asymptotic stability of Hopfield neural networks. This is followed by a robustness analysis of the class of neural networks considered. The results obtained are then applied to an optimization problem.This work was supported in part by the National Science Foundation under Grant ECS 93-19352.     

一类新的模式识别联想神经网络

本文提出一类可用于模式识别的联想神经网络的综合方法,这类网络结构不受对称联接的限制,网络保证了要求的M类模式的稳定形成,且网络的容量远远超过Hopfield的联想神经网络,网络渐近稳定平衡点的吸引特性使受噪声污染的模式能得以正确恢复,体现了神经网络的非线性滤波性质。文中给出了综合一个这类联想网络计算机模拟以及模式识别的例子。     

多时滞神经网络的全局指数稳定性

多时滞神经网络是一种特殊结构的动力系统,其全局指数稳定性在实际应用中起着非常重要的作用.本文通过构建Lyapunov函数的方法,对一类一般多时滞神经网络的全局指数稳定进行了分析,得到了多时滞神经网络全局指数稳定性的几个充分条件,本文的结果涵盖并推广了最近文献的结论,并给出实例进行数字仿真说明本文结果的有效性.     

联想记忆神经网络吸收区域的估计

本文对于Hopfield型联想记忆神经网络模型,给出了吸收区域估计的解析表达式。这对于具有多个平衡位置的网络实现联想记忆和优化计算都是重要的问题。     

具有时滞的高阶Hopfield型神经网络的稳定性

通过Lyapunov泛函的方法，对具有时滞的高阶连续型Hopfield神经网络平衡点的稳定性进行分析，利用Razumikhin定理得到平衡点全局一致渐近稳定的时滞相关与时滞无关充分条件。     

神经网络与光计算

介绍了近年来正在兴起的光神经计算的研究动态。着重讨论了神经网络与光技术、光神经计算、光联想学习和联想记忆系统,光神经器件及目前发展光神经计算的有关问题等。     

Estimating the storage capacity of space-varying cellular neuralnetworks

The capacity of associative memories based on space-varying, nonreciprocal, discrete-time cellular neural networks (CNNs) is investigated. The capacity is defined as the maximum number of random bipolar prototypes which can be stored with probability larger than a suitable threshold. It is shown that the capacity of the CNN is actually determined by the cells with the smallest number of connections, i.e. those located at the corners of the rectangular array. A simple empirical formula is presented which enables a prediction to be made as to the capacity of the CNN associative memory as a function of the neighbourhood radius and of the stability margin     

Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks

A set of sufficient and necessary conditions are presented for global exponential stability (GES) of a class of generic discrete-time recurrent neural networks. By means of the uncovered conditions, GES and convergence properties of the neural networks are analyzed quantitatively. It is shown that exact equivalences exist among the GES property of the neural networks, the contractiveness of the deduced nonlinear operators, and the global asymptotic stability (GAS) of the neural networks plus the spectral radius of Jacobian matrix of the neural networks at the unique equilibrium point less than one. When the neural networks have small state feedback coefficients, it is shown further that the infimum of exponential bounds of the trajectories of the neural networks equals exactly the spectral radius of Jacobian matrix of the neural networks at the unique equilibrium point. The obtained results are helpful in understanding essence of GES and clarifying difference between GES and GAS of the discrete-time recurrent neural networks.