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題名 Patterns generation and transition matrices in multi-dimensional lattice models
作者 班榮超
Ban, Jung-Chao
Lin, Song-Sun
貢獻者 應數系
日期 2005-08
上傳時間 22-六月-2020 13:43:04 (UTC+8)
摘要 In this paper we develop a general approach for investigating pattern generation problems in multi-dimensional lattice models. Let S be a set of p symbols or colors, ZN a fixed finite rectangular sublattice of Zd, d ≥ 1 and N a d-tuple of positive integers. Functions U : Zd → S and UN : ZN → S are called a global pattern and a local pattern on ZN , respectively. We introduce an ordering matrix XN for ΣN , the set of all local patterns on ZN . For a larger finite lattice ZN˜ , N˜ ≥ N, we derive a recursion formula to obtain the ordering matrix XN˜ of ΣN˜ from XN . For a given basic admissible local patterns set B ⊂ ΣN , the transition matrix TN (B) is defined. For each N˜ ≥ N denoted by ΣN˜ (B) the set of all local patterns which can be generated from B, the cardinal number of ΣN˜ (B) is the sum of entries of the transition matrix TN˜ (B) which can be obtained from TN (B) recursively. The spatial entropy h(B) can be obtained by computing the maximum eigenvalues of a sequence of transition matrices Tn(B). The results can be applied to study the set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.
關聯 Discrete and Continuous Dynamical Systems, Vol.13, No.3, pp.637-658
資料類型 article
DOI http://dx.doi.org/10.3934/dcds.2005.13.637
dc.contributor 應數系
dc.creator (作者) 班榮超
dc.creator (作者) Ban, Jung-Chao
dc.creator (作者) Lin, Song-Sun
dc.date (日期) 2005-08
dc.date.accessioned 22-六月-2020 13:43:04 (UTC+8)-
dc.date.available 22-六月-2020 13:43:04 (UTC+8)-
dc.date.issued (上傳時間) 22-六月-2020 13:43:04 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/130202-
dc.description.abstract (摘要) In this paper we develop a general approach for investigating pattern generation problems in multi-dimensional lattice models. Let S be a set of p symbols or colors, ZN a fixed finite rectangular sublattice of Zd, d ≥ 1 and N a d-tuple of positive integers. Functions U : Zd → S and UN : ZN → S are called a global pattern and a local pattern on ZN , respectively. We introduce an ordering matrix XN for ΣN , the set of all local patterns on ZN . For a larger finite lattice ZN˜ , N˜ ≥ N, we derive a recursion formula to obtain the ordering matrix XN˜ of ΣN˜ from XN . For a given basic admissible local patterns set B ⊂ ΣN , the transition matrix TN (B) is defined. For each N˜ ≥ N denoted by ΣN˜ (B) the set of all local patterns which can be generated from B, the cardinal number of ΣN˜ (B) is the sum of entries of the transition matrix TN˜ (B) which can be obtained from TN (B) recursively. The spatial entropy h(B) can be obtained by computing the maximum eigenvalues of a sequence of transition matrices Tn(B). The results can be applied to study the set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.
dc.format.extent 383718 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Discrete and Continuous Dynamical Systems, Vol.13, No.3, pp.637-658
dc.title (題名) Patterns generation and transition matrices in multi-dimensional lattice models
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.3934/dcds.2005.13.637
dc.doi.uri (DOI) http://dx.doi.org/10.3934/dcds.2005.13.637