Limitation on stabilizing plane waves via time-delay feedback.

@article{Harrington2001LimitationOS,
  title={Limitation on stabilizing plane waves via time-delay feedback.},
  author={Ilan Harrington and Joshua E. S. Socolar},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2001},
  volume={64 5 Pt 2},
  pages={056206}
}
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… CONTINUE READING