Dynamic analysis of coupled Binary Sawtooth and Sawtooth and Cow patch cellular neural networks

Nature abounds with complex patterns emerging from biological, chemical, physical and social systems. Cellular Neural Networks (CNNs) may produce patterns similar to those found in nature, which implies that CNNs may be use as protoypes to describe some systems in nature. The Binary Sawtooth and Cow patch CNNs introduced by Chua et al. can generate pattern that sawtooths and cow patches coexist from any random initial pattern. In order to investigate the characteristics of the Binary Sawtooth and Cow patch CNNs, this study introduces concepts of so-called inherent (final) active, inherent (final) passive, and inherent (final) neutral for pattern pixels, and proposes Global Task and Local Rules of the Binary Sawtooth and Cow patch CNNs, and establishes a set of theorems. Three simulation examples have been carried out to verily the effectiveness of theoretical results.