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Title: Delayed feedback control and phase reduction of unstable quasi-periodic orbits.
Authors: Ichinose, Natsuhiro  kyouindb  KAKEN_id
Komuro, Motomasa
Author's alias: 市瀬, 夏洋
Issue Date: Sep-2014
Publisher: American Institute of Physics
Journal title: Chaos
Volume: 24
Issue: 3
Thesis number: 033137
Abstract: The delayed feedback control (DFC) is applied to stabilize unstable quasi-periodic orbits (QPOs) in discrete-time systems. The feedback input is given by the difference between the current state and a time-delayed state in the DFC. However, there is an inevitable time-delay mismatch in QPOs. To evaluate the influence of the time-delay mismatch on the DFC, we propose a phase reduction method for QPOs and construct a phase response curve (PRC) from unstable QPOs directly. Using the PRC, we estimate the rotation number of QPO stabilized by the DFC. We show that the orbit of the DFC is consistent with the unstable QPO perturbed by a small state difference resulting from the time-delay mismatch, implying that the DFC can certainly stabilize the unstable QPO.
Rights: © 2014 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
URI: http://hdl.handle.net/2433/191009
DOI(Published Version): 10.1063/1.4896219
PubMed ID: 25273217
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