Limitation on stabilizing plane waves via time-delay feedback.
Previous work has demonstrated the possibility of stabilizing plane wave solutions of one-dimensional systems using a spatially local form of time-delayed feedback. We show that the natural extension of this method to two-dimensional systems fails due to the presence of torsion-free unstable perturbations. Linear stability analysis of the complex Ginzburg-Landau equation reveals that long wavelength, transverse wave instabilities cannot be suppressed by the method of extended time-delay autosynchronization. The conclusion follows from symmetry considerations and therefore applies to a wide class of models with simple plane wave solutions.
Harrington
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Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA.
Socolar
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