On the structure of multi-layer cellular neural networks

Abstract

Let Y subset of {-1, 1}(Z infinity xn) be the mosaic solution space of an n-layer cellular neural network. We decouple Y into n subspaces, say Y-(1), Y-(2), ... , Y-(n), and give a necessary and sufficient condition for the existence of factor maps between them. In such a case, Y-(i) is a sofic shift for 1 <= i <= n. This investigation is equivalent to study the existence of factor maps between, two sofic shifts. Moreover, we investigate whether Y-(i) and Y-(j) are topological conjugate, strongly shift equivalent, shift equivalent, or finitely equivalent via the well-developed theory in symbolic dynamical systems. This clarifies, in a multi-layer cellular neural network, each layer's structure. As an extension, we can decouple Y into arbitrary k-subspaces. where 2 <= k <= n, and demonstrates each subspace's structure. (C) 2012 Elsevier Inc. All rights reserved.