Template design methods for binary stable cellular neural networks

Stable cellular neural networks with binary outputs implement a non‐linear mapping between sets of input and output images. Such a mapping is studied in detail. We prove two theorems: the first one yields a sufficient condition in order that the non‐linear mapping be well‐defined; the second one yields a condition, that allows to describe the mapping through a simple algorithm based on the sign of the initial derivatives. Then we enunciate two additional theorems and two corollaries, that identify the class of templates satisfying the above condition: such a class is shown to be rather large and include, as particular cases, the monotonic templates, and several kinds of non‐monotonic templates. Finally,a rigorous design procedure is proposed.