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https://ah.lib.nccu.edu.tw/handle/140.119/130200
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: | 四月-2012 | 上傳時間: | 22-六月-2020 | 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: | https://doi.org/10.1016/j.jde.2012.01.006 |
Appears in Collections: | 期刊論文 |
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