On the margin of complete stability for a class of cellular neural networks

In this paper, the dynamical behavior of a class of third-order competitive cellular neural networks (CNNs) depending on two parameters, is studied. The class contains a one-parameter family of symmetric CNNs, which are known to be completely stable. The main result is that it is a generic property within the family of symmetric CNNs that complete stability is robust with respect to (small) nonsymmetric perturbations of the neuron interconnections. The paper also gives an exact evaluation of the complete stability margin of each symmetric CNN via the characterization of the whole region in the two-dimensional parameter space where the CNNs turn out to be completely stable. The results are established by means of a new technique to investigate trajectory convergence of the considered class of CNNs in the nonsymmetric case.