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.     

离散Hopfield联想记忆神经网络的渐近行为

该文对一类离散Hopfield联想记忆神经网络的渐近行为进行了讨论，首先提出这类I／O函数取为Sigmoid型函数的离散Hopfield联想记忆神经网络的数学模型，讨论并给出了这种模型的一系列性质，例如运动轨迹的有界性，平衡点的唯一性以及渐近稳定性等，得到了平衡点渐近稳定的充分条件，检验这种神经网络模型的渐近稳定性，只需要测试一个特定矩阵的定性性质或特定不等式即可，这些结果可用于离散Hopfield联想记忆神经网络的综合过程。     

具有内连接的指数多值双向联想记忆模型

C_CWang的多值指数双向联想记忆模型 (MVeBAM)是一种高存储容量的联想神经网络. 本文在MVe BAM的基础上通过引入自相关项 (或内连接 )提出了一个新的具有内连接的多值指数双向联想记忆模型, 推广了MVeBAM. 通过定义简单的能量函数证明了其在同、异步方式下的稳定性, 从而保证了所学模式对成为被推广的MVeBAM(EMVeBAM)的稳定点. 最后, 计算机模拟证实了EMVeBAM比MVeBAM具有更高的存储容量和更好的纠错性能.     

一种新的双向联想记忆神经网络学习算法

文章提出了一种基于遗传算法的按`位'加权双向联想记忆神经网络(BAM)的学习算法.根据判定BAM网络稳定模式和容错能力的充分条件,推出了求取按位加权BAM加权系数的优化目标函数,之后作者给出了求解此目标函数的遗传算法.二值图象模式存储、联想记忆的计算机实验结果表明,文中所提出的方法能有效地提高网络的存储能力和容错能力.     

基于离散双向联想记忆神经网络的多元通信系统

针对噪声导致非线性数字通信系统传输信号的差错概率增加的问题，提出一种基于离散双向联想记忆（BAM）神经网络的多元通信系统。首先，根据需要传输的信号，选取适当的神经元数量和记忆向量，计算权值矩阵，并生成BAM神经网络；然后将多元信号映射为具有调制幅度的初始输入向量并不断输入系统，通过神经网络进行循环迭代，并向各神经元添加高斯噪声，之后按照码元间隔采样输出并在无损信道中传输，接收端依据判决规则译码判决；最后在图像处理领域，利用所提系统传输图像压缩后的数据并解码恢复图像。仿真结果表明，对于码元间隔较大的弱调制信号，随着噪声强度的增加，差错概率先减后增，随机共振现象比较明显；差错概率还与信号的进制数呈正相关关系，与信号幅度、码元间隔和神经元个数呈负相关关系，某些条件下，差错概率可以达到0。以上结果表明BAM神经网络可以通过噪声改善数字通信系统的可靠性。另外，解码恢复图像的相似度显示了适量噪声对图像恢复效果的改善，扩展了BAM神经网络和随机共振在图像压缩编码中的应用。     

带区间时变时滞的BAM神经网络渐近稳定性

针对一类具有区间时滞和随机干扰的BAM神经网络的全局渐近稳定性问题,通过构造合适的Lyapunov-Krasovskii泛函,应用随机分析和自由权值矩阵方法,并考虑时滞区间范围,得到了新的稳定性充分条件。该条件能够保证时滞BAM神经网络在均方意义下是全局渐近稳定的,同时适用于快时滞和慢时滞,其适用范围更广。最后,通过一个仿真实例证明了定理的有效性。     

带区间时变时滞的BAM神经网络渐近稳定性

针对一类具有区间时滞和随机干扰的BAM神经网络的全局渐近稳定性问题,通过构造合适的Lyapunov-Krasovskii泛函,应用随机分析和自由权值矩阵方法,并考虑时滞区间范围,得到了新的稳定性充分条件。该条件能够保证时滞BAM神经网络在均方意义下是全局渐近稳定的,同时适用于快时滞和慢时滞,其适用范围更广。最后,通过一个仿真实例证明了定理的有效性。     

中立联想记忆神经网络鲁棒稳定性新准则

针对一类具有离散时滞和参数范数有界的不确定性中立联想记忆神经网络的全局渐近鲁棒稳定性问题进行了研究.通过应用范数理论和矩阵不等式分析方法,并构造合适的Lyapunov-Krasovskii泛函,推导出了与时滞无关的新稳定性判定准则,用于保证神经网络的平衡点是全局渐近鲁棒稳定的.该准则中包含的未知参数少、计算复杂度低,易于验证.仿真算例验证了新判定准则的有效性.     

时滞标准神经网络模型及其应用

提出一种新的神经网络模型---时滞标准神经网络模型(DSNNM),它由线性动力学系统和有界静态时滞非线性算子连接而成.利用不同的Lyapunov泛函和S方法推导出DSNNM全局渐近稳定性和全局指数稳定性的充分条件,这些条件可表示为线性不等式(LMI)形式.大多数时滞(或非时滞)动态神经网络(DANN)稳定性分析或神经网络控制系统都可以转化为DSNNM,以便用统一的方法进行稳定性分析或镇定控制.从DSNNM应用于时滞联想记忆(BAM)神经网络的稳定性分析以及PH中和过程神经控制器的综合实例,可以看出,得到的稳定性判据扩展并改进了以往文献中的稳定性定理,而且可将稳定性分析推广到非线性控制系统的综合.     

离散指数型BAM网络的记忆容量

基于Kosko的双向联想记忆模型BAM(bidirectional associative memory)原理,本文提出了一个离散指数型双向联想记忆模型.通过理论分析证实,该模型的记忆容量远远大于BAM的记忆容量.本文给出了指数型BAM记忆容量的下界.     

Global exponential stability of bidirectional associative memory neural networks with time delays.

In this paper, we consider delayed bidirectional associative memory (BAM) neural networks (NNs) with Lipschitz continuous activation functions. By applying Young's inequality and Hoelder's inequality techniques together with the properties of monotonic continuous functions, global exponential stability criteria are established for BAM NNs with time delays. This is done through the use of a new Lyapunov functional and an M-matrix. The results obtained in this paper extend and improve previous results.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

不确定时滞BAM神经网络的鲁棒稳定性

利用自由权值矩阵和不等式分析技巧,研究了一类不确定时滞BAM神经网络的鲁棒稳定性问题。通过构造适当的Lya-punov泛函,对于所有允许的不确定性,以线性矩阵不等式形式给出了时滞BAM神经网络的全局鲁棒稳定性判据,该判据能够利用Matlab的LMI工具箱很容易地进行检验。此外,仿真示例进一步证明了判据的有效性。     

Existence and Exponential Stability of Periodic Solution for BAM Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays

In this paper, BAM fuzzy Cohen–Grossberg neural networks with mixed delays are considered. Using M-matrix theory and differential inequality techniques, some sufficient conditions for the existence and exponential stability of periodic solution to the neural networks are established. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to illustrate the effectiveness of our results obtained.     

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

     

噪声环境中时延区间CNN网络鲁棒稳定性

由于采用大规模集成电路方法实现细胞神经网络(cellular neural networks,CNN),其 电路所产生的噪声不可避免,实际的网络都是在噪声环境中进行工作的,弄清楚这些随机干扰 是如何影响网络的稳定性,在网络设计时非常关键.利用鞅收敛定理、李雅普诺夫直接法和矩阵 分析的方法,研究了白噪声干扰下时延区间细胞神经网络承受扰动的能力,得到了仅依赖系统 参数的充分性代数判据.所得结果在系统设计时检验较为方便.     

BAM神经网络周期解的存在性与稳定性

利用不动点理论、Lyapunov泛函,研究了具变时滞的BAM神经网络周期解的存在性、唯一性和全局指数稳定性问题。所得的充分判别标准由线性矩阵不等式所表示,可以较容易地由Matlab进行验证。仿真实例表明,得到的判据是有效的。     

Robust stability of interval bidirectional associative memory neural network with time delays.

In this paper, the conventional bidirectional associative memory (BAM) neural network with signal transmission delay is intervalized in order to study the bounded effect of deviations in network parameters and external perturbations. The resultant model is referred to as a novel interval dynamic BAM (IDBAM) model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of unique equilibrium and robust stability are derived. These results are fairly general and can be verified easily. To go further, we extend our investigation to the time-varying delay case. Some robust stability criteria for BAM with perturbations of time-varying delays are derived. Besides, our approach for the analysis allows us to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as the usual C1-smooth sigmoids. We believe that the results obtained have leading significance in the design and application of BAM neural networks.     

Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.