Stable Patterns Realized by a Class of One-Dimensional Two-Layer CNNs
Norikazu Takahashi, M. Nagayoshi, S. Kawabata, Tetsuo Nishi · IEEE Transactions on Circuits and Systems I Regular Papers · 2008
Stable patterns that can be realized by a class of 1D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets.