Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/85661
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Type: Journal article
Title: Accurate control of hyperbolic trajectories in any dimension
Author: Balasuriya, S.
Padberg-Gehle, K.
Citation: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2014; 90(3):032903-1-032903-9
Publisher: American Physical Society
Issue Date: 2014
ISSN: 1539-3755
1550-2376
Statement of
Responsibility: 
Sanjeeva Balasuriya, Kathrin Padberg-Gehle
Abstract: The unsteady (nonautonomous) analog of a hyperbolic fixed point is a hyperbolic trajectory, whose importance is underscored by its attached stable and unstable manifolds, which have relevance in fluid flow barriers, chaotic basin boundaries, and the long-term behavior of the system. We develop a method for obtaining the unsteady control velocity which forces a hyperbolic trajectory to follow a user-prescribed variation with time. Our method is applicable in any dimension, and accuracy to any order is achievable.We demonstrate and validate our method by (1) controlling the fixed point at the origin of the Lorenz system, for example, obtaining a user-defined nonautonomous attractor, and (2) the saddle points in a droplet flow, using localized control which generates global transport.
Keywords: Models, Theoretical; Physical Phenomena; Hydrodynamics
Rights: © 2014 American Physical Society
RMID: 0030008070
DOI: 10.1103/PhysRevE.90.032903
Grant ID: http://purl.org/au-research/grants/arc/FT130100484
Appears in Collections:Mathematical Sciences publications

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