A study on limit cycles in nearly symmetric cellular neural networks

It is known that symmetric cellular neural networks (CNNs) are completely stable, i.e., each trajectory converges towards some equilibrium point. The paper addresses the issue of the loss of CNN complete stability caused by errors in the implementation of the nominal symmetric interconnections. The main result is a structural condition which implies the existence of stable limit cycles generated via Hopf bifurcations, even for arbitrarily small perturbations of the nominal interconnections. Furthermore, analytic results providing an approximate relationship between the limit cycle features and the fundamental CNN parameters are presented.