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.