政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/130202

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 113648/144635 (79%)
Visitors : 51585474 Online Users : 884

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer

政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/130202

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/130202

Title:	Patterns generation and transition matrices in multi-dimensional lattice models
Authors:	班榮超 Ban, Jung-Chao Lin, Song-Sun
Contributors:	應數系
Date:	2005-08
Issue Date:	2020-06-22 13:43:04 (UTC+8)
Abstract:	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.
Relation:	Discrete and Continuous Dynamical Systems, Vol.13, No.3, pp.637-658
Data Type:	article
DOI 連結:	http://dx.doi.org/10.3934/dcds.2005.13.637
DOI:	10.3934/dcds.2005.13.637
Appears in Collections:	[應用數學系] 期刊論文

Files in This Item:

File	Description	Size	Format
114.pdf		374Kb	Adobe PDF2	252	View/Open

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

Loading...