On the Structure of Two-Layer Cellular Neural Networks

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let Y⊆{-1,1} ∞×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.

Original languageEnglish
Title of host publicationDifferential and Difference Equations with Applications - Contributions from the International Conference on Differential and Difference Equations and Applications
PublisherSpringer New York LLC
Pages265-273
Number of pages9
ISBN (Print)9781461473329
DOIs
StatePublished - 1 Jan 2013
EventInternational Conference on Differential and Difference Equations and Applications - Ponta Delgada, Portugal
Duration: 4 Jul 20118 Jul 2011

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume47
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Differential and Difference Equations and Applications
CountryPortugal
CityPonta Delgada
Period4/07/118/07/11

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  • Cite this

    Ban, J. C., Chang, C. H., & Lin, S-S. (2013). On the Structure of Two-Layer Cellular Neural Networks. In Differential and Difference Equations with Applications - Contributions from the International Conference on Differential and Difference Equations and Applications (pp. 265-273). (Springer Proceedings in Mathematics and Statistics; Vol. 47). Springer New York LLC. https://doi.org/10.1007/978-1-4614-7333-6_20