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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/130200

Title:	On the structure of multi-layer cellular neural networks
Authors:	班榮超 Ban, Jung-Chao Chang, Chih-Hung Lin, Song-Sun
Contributors:	應數系
Keywords:	Sofic shift;Strong shift equivalence;Shift equivalence;Finite equivalence;Dimension group
Date:	2012-04
Issue Date:	2020-06-22 13:42:34 (UTC+8)
Abstract:	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.
Relation:	Journal of Differential Equations, Vol.252, No.8, pp.4563-4597
Data Type:	article
DOI link:	https://doi.org/10.1016/j.jde.2012.01.006
DOI:	10.1016/j.jde.2012.01.006
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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