Some Remarks on the Stability of Discrete-Time Complex-Valued Multistate Hopfield Neural Networks

Resumen

In this paper, we review three discrete-time complex-valued Hopfield neural networks (CvMHNNs) proposed recently in the literature. Contrary to what has been stated, we provide examples in which the sequences produced by these CvMHNN fails to converge under the usual conditions on the synaptic weight matrix, that is, the synaptic weight matrix is hermitian with non-negative diagonal elements. Furthermore, we present one CvMHNN model that always settle down to a stationary state under the usual conditions on the synaptic weights.