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THREE-DIMENSIONAL CELLULAR NEURAL NETWORKS AND PATTERN GENERATION PROBLEMS

Department of Mathematics, National Hualien University of Education, Hualien 97003, Taiwan

This research is partially supported by the National Science Council, R.O.C. (Contract No. NSC 95-2115-M-026-003) and the National Center for Theoretical Sciences.

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SONG-SUN LIN

Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan

The author would like to thank the National Science Council, R.O.C. (Contract No. 95-2115-M-009) and the National Center for Theoretical Sciences for partially supporting this research.

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YIN-HENG LIN

Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan

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https://doi.org/10.1142/S0218127408020781Cited by:5 (Source: Crossref)

Abstract

This work investigates three-dimensional pattern generation problems and their applications to three-dimensional Cellular Neural Networks (3DCNN). An ordering matrix for the set of all local patterns is established to derive a recursive formula for the ordering matrix of a larger finite lattice. For a given admissible set of local patterns, the transition matrix is defined and the recursive formula of high order transition matrix is presented. Then, the spatial entropy is obtained by computing the maximum eigenvalues of a sequence of transition matrices. The connecting operators are used to verify the positivity of the spatial entropy, which is important in determining the complexity of the set of admissible global patterns. The results are useful in studying a set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.

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