Spatial and temporal feedback control of traveling wave solutions of the two-dimensional complex Ginzburg-Landau equation
arXiv:nlin/0701007 · doi:10.1016/j.physd.2007.07.011
Abstract
Previous work has shown that Benjamin-Feir unstable traveling waves of the complex Ginzburg-Landau equation (CGLE) in two spatial dimensions cannot be stabilized using a particular time-delayed feedback control mechanism known as `time-delay autosynchronisation'. In this paper, we show that the addition of similar spatial feedback terms can be used to stabilize such waves. This type of feedback is a generalization of the time-delay method of Pyragus (Phys. Letts. A 170, 1992) and has been previously used to stabilize waves in the one-dimensional CGLE by Montgomery and Silber (Nonlinearity 17, 2004). We consider two cases in which the feedback contains either one or two spatial terms. We focus on how the spatial terms may be chosen to select the direction of travel of the plane waves. Numerical linear stability calculations demonstrate the results of our analysis.
arXiv comment21 pages, 7 figures, to appear in Physica D
References in corpus (5)
- Refuting the odd number limitation of time-delayed feedback control
- Controlling spatiotemporal dynamics with time-delay feedback
- Feedback Control of Traveling Wave Solutions of the Complex Ginzburg Landau Equation
- Controlling spatiotemporal chaos in oscillatory reaction-diffusion systems by time-delay autosynchronization
- Continuous control of ionization wave chaos by spatially derived feedback signals
Cited by in corpus (8)
- Control of spatiotemporal patterns in the Gray-Scott model
- Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control
- Instabilities of localized structures in dissipative systems with delayed feedback
- Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation
- Pattern-Selective Feedback Stabilization of Ginzburg--Landau Spiral Waves
- Stabilisation of long-period periodic orbits using time-delayed feedback control
- Stability of plane wave solutions in complex Ginzburg-Landau equation with delayed feedback
- Noise-induced peak intensity fluctuations in class B laser systems