On the Templates Corresponding to Cycle-Symmetric Connectivity in Cellular Neural Networks

In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling laws. These laws are characterized by the so-called templates which express the local interaction weights among cells. Recently, the complete stability for CNN has been extended from symmetric connections to cycle-symmetric connections. In this presentation, we investigate a class of templates which are obtained from two-dimensional models and have uniform local feedback behaviors. We find necessary and sufficient conditions for the class of templates to have cycle-symmetric connections. The complete stability for CNN is thus concluded.