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

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Title: A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
Authors: Arai, Zin Browse this author →KAKEN DB
Kalies, William Browse this author
Kokubu, Hiroshi Browse this author
Mischaikow, Konstantin Browse this author
Oka, Hiroe Browse this author
Pilarczyk, Paweł Browse this author
Keywords: database
dynamical system
Conley index
Morse decomposition
Leslie population models
combinatorial dynamics
multiparameter system
Issue Date: 2-Jul-2009
Publisher: Society for Industrial and Applied Mathematics
Journal Title: SIAM Journal on Applied Dynamical Systems
Volume: 8
Issue: 3
Start Page: 757
End Page: 789
Publisher DOI: 10.1137/080734935
Abstract: 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.
Rights: © 2009 Society for Industrial and Applied Mathematics
Type: article
URI: http://hdl.handle.net/2115/39480
Appears in Collections:創成研究機構 (Creative Research Institution) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 荒井 迅

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