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

Arai, Zin; Kalies, William; Kokubu, Hiroshi et al.

SIAM Journal on Applied Dynamical Systems, 2009, 8(3), 757-789

Permalink : https://hdl.handle.net/2115/39480

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アクセス権
open access
URI
https://hdl.handle.net/2115/39480
タイトル
A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
著者
Arai, Zin ; Kalies, William ; Kokubu, Hiroshi ; Mischaikow, Konstantin ; Oka, Hiroe ; Pilarczyk, Paweł
e-Rad_Researcher
80362432
著者名
Arai, Zin
著者名
Kalies, William
著者名
Kokubu, Hiroshi
著者名
Mischaikow, Konstantin
著者名
Oka, Hiroe
著者名
Pilarczyk, Paweł
言語
英語
キーワード
database
dynamical system
Conley index
Morse decomposition
Leslie population models
combinatorial dynamics
multiparameter system
発行日
2009-07-02
出版者
Society for Industrial and Applied Mathematics
収録物名
SIAM Journal on Applied Dynamical Systems
巻(号)
8(3)
ページ
757-789
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 http://chomp.rutgers.edu/database/, and the source code of the software used to obtain these results has also been made freely available.
資源タイプ
学術雑誌論文
出版タイプ
Version of Record
権利情報
© 2009 Society for Industrial and Applied Mathematics
PISSN
1536-0040
関連情報 (isIdenticalTo)
出版社版DOI
https://doi.org/10.1137/080734935