Convergence of discrete Hopfield-type neural networks with delay

An important property of discrete Hopfield-type neural networks is that it always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 when operating in a full parallel mode. In this paper, convergence theorems of discrete Hopfield-type neural networks with delay are obtained. Under a proper assumption, i.e., which weight matrix is a symmetric matrix, it is proved that any discrete Hopfield-type neural networks with delay will converge to a stable state operating in serial mode, and extends convergence theorems in earlier works. The authors also relate the maximum of bivariate energy function to the stable state of neural networks with delay. In other words, this network can converge to a stable state in only one delay step while the energy function has converged. The correlation between convergence of the energy function and convergence corresponding to the network is also presented