Limitation on stabilizing plane waves via time-delay feedback - art. no. 056206

Previous work has demonstrated the possibility of stabilizing plane wave so lutions of one-dimensional systems using a spatially local form of time-del ayed feedback. We show that the natural extension of this method to two-dim ensional systems fails due to the presence of torsion-free unstable perturb ations. Linear stability analysis of the complex Ginzburg-Landau equation r eveals that long wavelength, transverse wave instabilities cannot be suppre ssed by the method of extended time-delay autosynchronization. The conclusi on follows from symmetry considerations and therefore applies to a wide cla ss of models with simple plane wave solutions.