標題: On the structure of multi-layer cellular neural networks
作者: Ban, Jung-Chao
Chang, Chih-Hung
Lin, Song-Sun
應用數學系
Department of Applied Mathematics
關鍵字: Sofic shift;Strong shift equivalence;Shift equivalence;Finite equivalence;Dimension group
公開日期: 15-Apr-2012
摘要: Let Y subset of {-1, 1}(Z infinity xn) 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. (C) 2012 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jde.2012.01.006
http://hdl.handle.net/11536/15527
ISSN: 0022-0396
DOI: 10.1016/j.jde.2012.01.006
期刊: JOURNAL OF DIFFERENTIAL EQUATIONS
Volume: 252
Issue: 8
起始頁: 4563
結束頁: 4597
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