Abstract
Let \(\mathbf{Y} \subseteq \{-1,{1\}}^{\mathbb{Z}_{\infty \times 2}}\) be the mosaic solution space of a two-layer cellular neural network (TCNN). We decouple Y into two subspaces, say Y (1) and Y (2), 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 i = 1,2. This investigation is equivalent to study the existence of factor maps between two sofic shifts. Moreover, we investigate whether Y (1) and Y (2) are topological conjugate, strongly shift equivalent, shift equivalent, or finitely equivalent via the well-developed theory in symbolic dynamical systems. This clarifies, in a TCNN, each layer’s structure.
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Ban, JC., Chang, CH., Lin, SS. (2013). On the Structure of Two-Layer Cellular Neural Networks. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_20
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DOI: https://doi.org/10.1007/978-1-4614-7333-6_20
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