Convergence of discrete neural networks in asynchronous updating mode

The discrete Hopfield neural network is a special kind of feedback neural networks, which can be widely used in the associative memory, combinatorial optimization, etc. The convergence of networks not only has an important theoretical significance, but also is the foundation for the applications of the neural networks. In this paper, the dynamic behavior of the discrete Hopfield neural network is mainly studied with the connection matrix without a symmetry assumption, and some new convergent conditions of the discrete neural networks in asynchronous updating mode are given. The obtained results here improve and generalize some existing results.