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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
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