### Abstract

Let Y⊆{-1,1}^{ℤ}
_{∞×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 language | English |
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Title of host publication | Differential and Difference Equations with Applications - Contributions from the International Conference on Differential and Difference Equations and Applications |

Publisher | Springer New York LLC |

Pages | 265-273 |

Number of pages | 9 |

ISBN (Print) | 9781461473329 |

DOIs | |

State | Published - 1 Jan 2013 |

Event | International Conference on Differential and Difference Equations and Applications - Ponta Delgada, Portugal Duration: 4 Jul 2011 → 8 Jul 2011 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 47 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Conference on Differential and Difference Equations and Applications |
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Country | Portugal |

City | Ponta Delgada |

Period | 4/07/11 → 8/07/11 |

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## Cite this

*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