Article ID Journal Published Year Pages File Type
1896897 Physica D: Nonlinear Phenomena 2012 9 Pages PDF
Abstract

The phase reduction method is applied to a general class of weakly perturbed time-delay systems exhibiting periodic oscillations. The adjoint equation with an appropriate initial condition for the infinitesimal phase response curve of a time-delay system is derived. The method is demonstrated numerically for the Mackey–Glass equation as well as for a chaotic Rössler system subject to a delayed feedback control (DFC). We show that the profile of the phase response curve of a periodic orbit stabilized by the DFC algorithm does not depend on the control matrix. This property is universal and holds for any dynamical system subject to the DFC.

► The phase reduction method is applied to weakly perturbed time-delay systems. ► The adjoint equation and initial condition for a phase response curve (PRC) are derived. ► Chaotic systems under delayed feedback control are considered. ► The profile of the PRC of a stabilized orbit does not depend of the control matrix.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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