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-Jun-2020 13:43:04 (UTC+8) | - |
dc.date.available | 22-Jun-2020 13:43:04 (UTC+8) | - |
dc.date.issued (上傳時間) | 22-Jun-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 | |