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Numerical multiscale methods for coupled oscillators
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
2009 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 7, no 3, 1387-1404 p.Article in journal (Refereed) Published
Abstract [en]

A multiscale method for computing the effective slow behavior of a system of weakly coupled nonlinear planar oscillators is presented. The oscillators may be either in the form of a periodic solution or a stable limit cycle. Furthermore, the oscillators may be in resonance with one another and thereby generate some hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the ordinary differential equation. The technique is more efficient than existing methods, and its advantages are demonstrated with examples. The algorithm follows the framework of the heterogeneous multiscale method.

Place, publisher, year, edition, pages
2009. Vol. 7, no 3, 1387-1404 p.
Keyword [en]
multiscale computation, nonlinear oscillators, resonance, phase locking, slow variables
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-72421DOI: 10.1137/070707245ISI: 000265777100010OAI: oai:DiVA.org:kth-72421DiVA: diva2:487644
Note
QC 20120201Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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