Accurate control of hyperbolic trajectories in any dimension
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Accurate control of hyperbolic trajectories in any dimension. / Balasuriya, Sanjeeva; Padberg-Gehle, Kathrin.
in: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Jahrgang 90, Nr. 3, 032903, 03.09.2014.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - Accurate control of hyperbolic trajectories in any dimension
AU - Balasuriya, Sanjeeva
AU - Padberg-Gehle, Kathrin
PY - 2014/9/3
Y1 - 2014/9/3
N2 - 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.
AB - 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.
KW - Mathematics
UR - http://www.scopus.com/inward/record.url?scp=84907484075&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.90.032903
DO - 10.1103/PhysRevE.90.032903
M3 - Journal articles
C2 - 25314500
AN - SCOPUS:84907484075
VL - 90
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 3
M1 - 032903
ER -