Dynamic analysis of coupled binary check-board — Strip 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 Check-board-Strip CNNs introduced by Chua et al. can generate pattern that check-boards and short single strips coexist from any random initial pattern. In order to investigate the characteristics of the Binary Check-board - Strip 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 Check-board - Strip CNNs, and establishes a set of theorems. Three simulation examples have been carried out to verify the effectiveness of theoretical results.