Stability analysis of discrete Hopfield Neural Networks with delay and its application

Discrete Hopfield Neural Networks (DHNNs) with delay, which can deal with temporal information, are a generalization of the DHNNs without delay. This paper investigates the convergence theorems in DHNNs with delay. We present two generalized updating rules, one for serial mode and the other for parallel mode. The convergence speed of these proposed updating rules is faster than existing updating rules. By means of the new network structure and its convergence theorems, we propose a local searching algorithm for combinatorial optimization. We also relate the maximum value of a bivariate energy function to the stable states of the DHNNs with delay. Furthermore, we describe an algorithm for the DHNNs with delay in which the delay term is regarded as noise, which has a higher convergence rate than usual algorithms in the Hopfield neural network without delay. One application is presented to demonstrate the higher rate of convergence of our algorithm.