Asymptotic behavior of discrete Hopfield networks

The discrete Hopfield neural network is a special kind of feedback neural networks. 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 various applications. The dynamic behavior of discrete Hopfield neural network is mainly studied in partial parallel mode by the use of the state transition equation and the energy function. One counter-example is given to illustrate one previous result in reference being error, and some new sufficient conditions for the networks converging towards stable states are investigated. The obtained results here further generalize some existing results on stability of the networks.