Authors : Runnian Ma , Youmin Xi and Jue Guo
Abstract: Discrete Hopfield neural network is one type of artificial neural network with very successful applications, and it is the foundations of researches on recurrent discrete neural networks. The stability analysis of discrete Hopfield neural networks not only has an important theoretical significance, but also can be widely used in the associative memory, combinatorial optimization, etc. In this paper, the dynamic behavior of asymmetric discrete Hopfield neural network is mainly studied in parallel mode, and some new simple stability conditions of the neural networks are presented by using the Lyapunov functional method and some analysis techniques. Also, some sufficient conditions for the networks having no stable state or converging towards a limit cycle with length 2 are given. Several theorems on dynamic behavior of the networks are proved. The results obtained here improved and extend the corresponding results given in the earlier references. Furthermore, we provide one method to analyze and design the stable discrete Hopfield neural networks.
Runnian Ma , Youmin Xi and Jue Guo , 2005. Dynamic Behavior of Discrete Hopfield Neural Networks . Asian Journal of Information Technology, 4: 9-15.