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タイトル
  • A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
作成者

Arai, Zin

Kalies, William

Kokubu, Hiroshi

Mischaikow, Konstantin

Oka, Hiroe

Pilarczyk, Paweł

権利情報
    • © 2009 Society for Industrial and Applied Mathematics
主題
  • Other database
  • Other dynamical system
  • Other Conley index
  • Other Morse decomposition
  • Other Leslie population models
  • Other combinatorial dynamics
  • Other multiparameter system
  • NDC 007
内容注記
Other
  • 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Society for Industrial and Applied Mathematics
日付 Issued 2009-07-02
言語eng
資源タイプjournal article
出版タイプVoR
資源識別子 URI http://hdl.handle.net/2115/39480
関連
  • isIdenticalTo DOI https://doi.org/10.1137/080734935
収録誌情報
    • ISSN 1536-0040
    • SIAM Journal on Applied Dynamical Systems
    8(3), 757-789
ファイル
コンテンツ更新日時2018-11-02T01:24:07Z