Spatio-temporal patterns in cellular neural networks

In this paper, we study the patterns that can be generated in Cellular Neural Networks. In particular, we consider first 1-dim. arrays with nearest neighbor coupling and periodic boundary conditions and show that an exponential number of equilibria exists, when the template is close to symmetric, but not when the template is close to antisymmetric: in this case periodic solutions are present. Finally we focus on the dynamics of pattern formation in 2-dim. arrays with symmetric template.