Robustness of complete stability: Hopfield model vs. cellular neural network model

The paper investigates how the maximum gain of the neuron activation influences robustness of complete stability of nominal symmetric neural networks with respect to perturbations of the neuron interconnections. For a class of third-order neural networks it is shown that high values of the gain lead to an extremely small complete stability margin for all nominal symmetric neural networks. This implies that low gain neurons as those employed in the standard Cellular Neural Networks are preferable, in view of the considered robustness issue, with respect to high-gain neurons as those typically employed in Hopfield neural networks.