PMID: 15244906Jul 13, 2004Paper

Domain of attraction for stabilized orbits in time delayed feedback controlled Duffing systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kohei Yamasue, Takashi Hikihara

Abstract

Time delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, this control method still has an open problem of estimating domain of attraction for target unstable periodic orbits. In this paper, we numerically discuss the domain of attraction in Duffing systems under the control method. The disturbance to initial conditions reveals that the domain of attraction possibly exhibits self-similar structures in its boundaries.

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Citations

Aug 9, 2006·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Kestutis Pyragas
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kohei Yamasue, Takashi Hikihara
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Asaki Saito, Keiji Konishi
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kestutis Pyragas, Viktoras Pyragas
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A TamaseviciusK Pyragas
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S Yanchuk, P Perlikowski
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Clemens von LoewenichWolfram Just
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ashraf A Zaher

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