Cellular neural networks: Mosaic pattern and spatial chaos

Abstract

We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z(2) on the plane R-2. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and epsilon, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic patterns and the parameter space (z, a; epsilon) can be completely characterized. This, in turn, addresses the so-called learning problem in CNNs. The complexities of mosaic patterns are also addressed.