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On the structure of multi-layer cellular neural networks

2012; Elsevier BV; Volume: 252; Issue: 8 Linguagem: Inglês

10.1016/j.jde.2012.01.006

1090-2732

Jung-Chao Ban, Chih-Hung Chang, Song-Sun Lin,

Nonlinear Dynamics and Pattern Formation

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.