Cellular neural networks: Space-dependent template, mosaic patterns and spatial chaos

Abstract

We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice Z(2) on the plane Z(2). We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on Z(2). Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p(1), p(2))-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.