TY - JOUR

T1 - On the structure of multi-layer cellular neural networks

AU - Ban, Jung Chao

AU - Chang, Chih Hung

AU - Lin, Song-Sun

PY - 2012/4/15

Y1 - 2012/4/15

N2 - Let Y⊆{-1,1} Z∞×n 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.

AB - Let Y⊆{-1,1} Z∞×n 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.

KW - Dimension group

KW - Finite equivalence

KW - Shift equivalence

KW - Sofic shift

KW - Strong shift equivalence

UR - http://www.scopus.com/inward/record.url?scp=84862815664&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2012.01.006

DO - 10.1016/j.jde.2012.01.006

M3 - Article

AN - SCOPUS:84862815664

VL - 252

SP - 4563

EP - 4597

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 8

ER -