Publications [#248383] of Joshua Socolar
- Harrington, I; Socolar, JE, Limitation on stabilizing plane waves via time-delay feedback.,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 64 no. 5 Pt 2
pp. 056206, ISSN 1539-3755 , [doi]
(last updated on 2019/06/17)
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.