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Exploring the qualitative behavior of uncertain dynamical systems : a computational approach
Publikationstyp
Journal Article
Date Issued
2011
Sprache
English
Author(s)
Gaull, Andreas
Journal
Volume
63
Issue
1-2
Start Page
285
End Page
310
Citation
Nonlinear Dynamics 63 (1-2): 285-310 (2011)
Publisher DOI
Scopus ID
Publisher
Springer Science + Business Media B.V
The global behavior of uncertain nonlinear systems by means of the cell mapping method is investigated. The systems under consideration are governed by ordinary differential equations where uncertainty is characterized by a bounded stationary noise process. In order to make cell mapping methods applicable to this particular situation generalizations of the theory become necessary. The numerical approach is based on a reformulation of the dynamics in terms of a Markov process whose qualitative behavior is analyzed. We demonstrate the usefulness of the presented scheme in the engineering field while addressing an example problem from technical mechanics.
Subjects
Cell mapping
Colored noise
Ergodic decomposition
Nonlinear dynamical systems
Transition operator
Uncertainty
DDC Class
510: Mathematics