On the universe of stable cellular neural networks

Abstract A cellular neural network (CNN) is a novel analogue circuit architecture with many desirable features. This paper extends previous stability results of CNNs to include classes of strictly sign‐symmetric and acyclic templates. We show that most of the 3×3 strictly sign‐symmetric templates are stable almost everywhere, with the unknown templates reduced to three classes. We also introduce template graphs and CNN graphs and utilize them to obtain results concerning stability and irreducibility of CNN templates.