Controlling extended systems with spatially filtered, time-delayed feedback

Details Controlling extended systems with spatially filtered, time-delayed feedback Controlling extended systems with spatially filtered, time-delayed feedback

1996-12-05

arxiv.org/abs/chao-dyn/9612013v1

Nonlinear Sciences

Chaotic Dynamics

9 pages REVTeX including 7 PostScript figures. To appear in Physical Review E

Scientific paper

10.1103/PhysRevE.55.2119

We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling wave state exists, but is a member of a nowhere stable family. Our scheme stabilizes this state, and directs the system towards it from realistic, distant and noisy initial conditions. As confirmed by numerical simulation, a linear stability analysis about the controlled state accurately predicts when the scheme is successful, and illustrates some key features of the control including the individual merit of, and interplay between, the spatial and temporal degrees of freedom in the control.

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