Oscillations in a class of third-order competitive cellular neural networks

We introduce a class of third-order cellular neural networks (CNNs) with competitive (inhibitory) interconnections between distinct neurons. We highlight the crucial importance of the neuron interconnection symmetry to ensure convergence of trajectories towards equilibrium points (complete stability). Indeed, the main contribution is that there are nonsymmetric competitive CNNs of this class whose interconnection matrix may be chosen arbitrarily close to a symmetric matrix, for which almost all trajectories persistently oscillating