离散时间反馈神经网络的渐近行为研究

Hopfield神经网络是一类应用非常成功的人工神经网络模型，它是研究这个反馈神经网络的基础．该文主要研究离散时间、连续状态的反馈神经网络，它是Hopfield神经网络的推广．众所周知，研究反馈神经网络的稳定性不仅被认为是神经网络最基本、最主要的问题之一，同时也是神经网络各种应用的基础．文中主要研究离散时间反馈神经网络的稳定性，给出了连接权矩阵非对称的并且输入-输出函数是一般的S-函数的新的渐近收敛性条件及相应的收敛性结论．所获结果不仅推广了一些已有的结论，而且为反馈神经网络的应用提供了一定的理论基础．

Study of Asymptotical Behavior in Discrete-Time Recurrent Neural Networks

Hopfield neural network is one type of artificial neural network with very successful applications, and it is the foundation of research on recurrent neural networks. This paper mainly studies one kind of discrete-time and continuous state recurrent neural networks, which is a generalization of Hopfield neural network. As it is known, the stability of recurrent neural networks is not only known to be one of the mostly basic problems, but also known to be bases of the network's various applications. In this paper, the stability of discrete-time recurrent neural networks is studied, and some new asymptotical stability conditions and relevant results are given, where the connection matrix of the networks is asymmetric and the input-output function is defined as a generalized sigmoid function. The obtained results not only generalize some existing results, but also provide a theoretical foundation of new applications of the recurrent neural networks.