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タイトル
  • en A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
作成者
    • en Kalies, William
    • en Kokubu, Hiroshi
    • en Mischaikow, Konstantin
    • en Oka, Hiroe
    • en Pilarczyk, Paweł
アクセス権 open access
権利情報
  • en © 2009 Society for Industrial and Applied Mathematics
主題
  • Other en database
  • Other en dynamical system
  • Other en Conley index
  • Other en Morse decomposition
  • Other en Leslie population models
  • Other en combinatorial dynamics
  • Other en multiparameter system
  • NDC 007
内容注記
  • Abstract en 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 http://chomp.rutgers.edu/database/, and the source code of the software used to obtain these results has also been made freely available.
出版者 en Society for Industrial and Applied Mathematics
日付
    Issued2009-07-02
言語
  • eng
資源タイプ journal article
出版タイプ VoR
資源識別子 HDL http://hdl.handle.net/2115/39480
関連
  • isIdenticalTo DOI https://doi.org/10.1137/080734935
収録誌情報
    • PISSN 1536-0040
      • en SIAM Journal on Applied Dynamical Systems
      • 8 3 開始ページ757 終了ページ789
ファイル
コンテンツ更新日時 2023-07-26