Convergence of discrete delayed Hopfield neural networks

The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode.