Stability for Discrete Hopfield Neural Networks with Delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. The dynamic behavior of discrete Hopfield neural networks with delay is mainly studied by using the method of defining energy function. The conditions for the networks with delay converging towards a limit cycle with length at most 2 and the conditions for the networks with delay converging towards a limit cycle with length 4 are respectively given. The obtained results here extend the existing results on stability of discrete Hopfield neural network with delay and without delay.