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.

STABILITY ANALYSIS OF DISCRETE-TIME HOPFIELD BAM NEURAL NETWORKS

In this paper, we consider the that discrete time Hopfield bidirectional associative memory(BAM) neural networks as a special Hopfield network model. We present a novel globally asymptotical stability and globally exponential stability analysis of the equilibrium points for discrete time Hopfield BAM neural networks. A constraint on the connection matrix has been found under which the neural network has a unique and asymptotically stable equilibrium point. Some sufficient conditions for the globally asymptotical stability and globally exponential stability of equilibrium points are derived using the existence of the positive diagonal solutions of the Lyapunov equations. These conditions can be used to design globally asymptoticaliy stable and globally exponentially stable networks. Analysis in this paper extends the previously known stability results.