On the structure of multi-layer cellular neural networks

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish
Pages (from-to)4563-4597
Number of pages35
JournalJournal of Differential Equations
Issue number8
StatePublished - 15 Apr 2012


  • Dimension group
  • Finite equivalence
  • Shift equivalence
  • Sofic shift
  • Strong shift equivalence

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