Dynamic analysis of coupled Gray Cow Patches and Checkerboards Coexist 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 used as prototypes to describe some systems in nature. The Gray Cow Patches and Checkerboards Coexist CNNs introduced by Chua et al. can generate patterns that cow patches and checkerboards coexist from any random initial patterns. In order to investigate the characteristics of the Gray Cow Patches and Checkerboards Coexist CNNs, this study introduces the concepts of so-called inherent (final) active, inherent (final) passive, and inherent (final) neutral for pattern pixels, and proposes the Global Task and Local Rules of the Gray Cow Patches and Checkerboards Coexist CNNs, and establishes a set of theorems and corollaries. Three simulation examples have been carried out to verify the effectiveness of theoretical results. Two instances reveal the characteristics of typicality.