政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/130200

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題名:	On the structure of multi-layer cellular neural networks
作者:	班榮超 Ban, Jung-Chao Chang, Chih-Hung Lin, Song-Sun
貢獻者:	應數系
關鍵詞:	Sofic shift;Strong shift equivalence;Shift equivalence;Finite equivalence;Dimension group
日期:	2012-04
上傳時間:	2020-06-22 13:42:34 (UTC+8)
摘要:	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.
關聯:	Journal of Differential Equations, Vol.252, No.8, pp.4563-4597
資料類型:	article
DOI 連結:	https://doi.org/10.1016/j.jde.2012.01.006
DOI:	10.1016/j.jde.2012.01.006
顯示於類別:	[應用數學系] 期刊論文

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