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A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems

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タイトル: A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
著者: Arai, Zin 著作を一覧する
Kalies, William 著作を一覧する
Kokubu, Hiroshi 著作を一覧する
Mischaikow, Konstantin 著作を一覧する
Oka, Hiroe 著作を一覧する
Pilarczyk, Paweł 著作を一覧する
キーワード: database
dynamical system
Conley index
Morse decomposition
Leslie population models
combinatorial dynamics
multiparameter system
発行日: 2009年 7月 2日
出版者: Society for Industrial and Applied Mathematics
誌名: SIAM Journal on Applied Dynamical Systems
巻: 8
号: 3
開始ページ: 757
終了ページ: 789
出版社 DOI: 10.1137/080734935
抄録: A generally applicable, automatic method for the efficient computation of a database of global dynamics of a multiparameter dynamical system is introduced. An outer approximation of the dynamics for each subset of the parameter range is computed using rigorous numerical methods and is represented by means of a directed graph. The dynamics is then decomposed into the recurrent and gradient-like parts by fast combinatorial algorithms and is classified via Morse decompositions. These Morse decompositions are compared at adjacent parameter sets via continuation to detect possible changes in the dynamics. The Conley index is used to study the structure of isolated invariant sets associated with the computed Morse decompositions and to detect the existence of certain types of dynamics. The power of the developed method is illustrated with an application to the two-dimensional density-dependent Leslie population model. An interactive visualization of the results of computations discussed in the paper can be accessed at the Web site, and the source code of the software used to obtain these results has also been made freely available.
Rights: © 2009 Society for Industrial and Applied Mathematics
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 荒井 迅


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