Stability of discrete Hopfield neural networks with time-delay

It is well known that Discrete Hopfield Neural Networks (DHNNs) without delay converge to a stable state. Due to this property, DHNNs without delay have wide potential applications to many fields such as associative memory devices and combinatorial optimization. For DHNNs with delay, which can deal with temporal information, it is a generalization of DHNN without delay, This paper investigates the convergence theorems of DHNNs with delay based on new updating modes, A new bivariate energy function is constructed which represents the relationships between application problems and DHNNs with delay. It is proved that DHNNs with delay will converge to stable state, These results are to extend the existing results corresponding to DHNNs without delay. We also relate maximum of this energy function to a stable state of DHNNs with delay. Furthermore, we describe DHNNs with delay-based algorithm in detailed.