Equilibrium and stability analysis of cellular neural networks

Some sufficient conditions for the existence of stable equilibrium points in cellular neural networks (CNNs), described by space-invariant templates, are presented. Such conditions exhibit the following advantages: 1) they exploit the key property of CNNs, i.e. the local interactions among the cells; 2) they can be verified by a simple examination of the template elements; 3) they give rise to constraints, that in most cases cover wider parameter sets than those available in the CNN literature. Extensive simulations show that the sufficient conditions also guarantee the network stability. This is in agreement with the fact that, so far, no example of unstable CNNs, possessing a stable equilibrium point, has been shown.