Cellular neural networks: Space-dependent template, mosaic patterns and spatial chaos

Jonq Juang; Shih Feng Shieh; Larry Turyn

doi:10.1142/S0218127402005510

Cellular neural networks: Space-dependent template, mosaic patterns and spatial chaos

Jonq Juang, Shih Feng Shieh, Larry Turyn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ² on the plane ℤ². We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ². Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.

Original language	English
Pages (from-to)	1717-1730
Number of pages	14
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
Issue number	8
DOIs	https://doi.org/10.1142/S0218127402005510
Publication status	Published - 2002 Aug

Keywords

Cellular Neural Networks
Space-dependent template
Spatial chaos

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S0218127402005510

Cite this

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abstract = "We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ2 on the plane ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.",

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AB - We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice ℤ2 on the plane ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.

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Cellular neural networks: Space-dependent template, mosaic patterns and spatial chaos

Abstract

Keywords

ASJC Scopus subject areas

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