Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/104919
Citations
Scopus Web of Science® Altmetric
?
?
Type: Journal article
Title: A numerical scheme for computing stable and unstable manifolds in nonautonomous flows
Author: Balasuriya, S.
Citation: International Journal of Bifurcation and Chaos, 2016; 26(14):1630041-1-1630041-22
Publisher: World Scientific
Issue Date: 2016
ISSN: 0218-1274
1793-6551
Statement of
Responsibility: 
Sanjeeva Balasuriya
Abstract: There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.
Keywords: Nonautonomous flow; stable manifold; unstable manifold; invariant manifold computation.
Rights: © World Scientific Publishing Company
RMID: 0030063903
DOI: 10.1142/S021812741630041X
Grant ID: http://purl.org/au-research/grants/arc/FT130100484
Appears in Collections:Mathematical Sciences publications

Files in This Item:
There are no files associated with this item.


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.