Stability Conditions for Discrete Delayed Hopfield Neural Networks

The stability of neural networks is not only the most basic and important problem but also the foundation of some neural network´s applications. In this paper, the stability of discrete delayed Hopfield neural networks is mainly investigated by constructing Lyapunov function and taking some inequality techniques into account. The sufficient conditions for discrete delayed Hopfield neural networks converging towards a limit cycle with 4-period are given. Also, some conditions for discrete delayed Hopfield neural networks neither having a stable state nor a limit cycle with 2-period are obtained. The obtained results here extend and improve some previously established results on the stability of discrete Hopfield neural network and the stability of discrete delayed Hopfield neural network in the literature.