Analysis and design of cellular neural networks

Cellular neural networks (CNNs) are large-scale systems described by locally coupled nonlinear differential equations. In most applications the connections are specified through space-invariant templates. CNNs with binary outputs are exploited for real time-image processing. So far, only a few methods have been proposed for designing binary CNNs. They are mainly based on the application of local rules, depending on the sign of the first order derivative of each cell, and they allow one to rigorously design only a small subset of templates. In this manuscript we show that the dynamic evolution of large class of binary CNNs can be predicted through a simple algorithm, based on the evaluation of higher order derivatives. Such an algorithm allows one to considerably extend the class of templates for which a design method exists.