Cellular Neural Networks: Pattern Formation and Spatial Chaos

We consider a Cellular Neural Network (CNN) with a bias term z in the integer lattice Z2 on the plane R 2 . We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and c, 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; c) can be completely characterized. This, in turn, addresses the so-called "Learning Problem" in CNNs. The complexities of mosaic is also studied.