The spatial entropy of two-dimensional subshifts of finite type

Jonq Juang; Song Sun Lin; Shih Feng Shieh; Wen Wei Lin

doi:10.1142/S0218127400001894

The spatial entropy of two-dimensional subshifts of finite type

Jonq Juang^*, Song Sun Lin, Shih Feng Shieh, Wen Wei Lin

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.

Original language	English
Pages (from-to)	2845-2852
Number of pages	8
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	10
Issue number	12
DOIs	https://doi.org/10.1142/S0218127400001894
Publication status	Published - 2000 Dec
Externally published	Yes

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S0218127400001894

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abstract = "In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.",

author = "Jonq Juang and Lin, {Song Sun} and Shieh, {Shih Feng} and Lin, {Wen Wei}",

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T1 - The spatial entropy of two-dimensional subshifts of finite type

AU - Juang, Jonq

AU - Lin, Song Sun

AU - Shieh, Shih Feng

AU - Lin, Wen Wei

PY - 2000/12

Y1 - 2000/12

N2 - In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.

AB - In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.

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The spatial entropy of two-dimensional subshifts of finite type

Abstract

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