Tracking Periodic Patterns into Spatiotemporal Chaotic Regimes

We show that unstable periodic solutions of spatially extended 2D systems, when weakly perturbed, can be stabilized by local feedback without spatial coupling. We argue through this finding that stable solutions can be tracked into unstable and spatiotemporal chaotic regimes by simply utilizing feedback control algorithms established for controlling temporal chaos in spatially constrained systems. We demonstrate numerically that the range of stable traveling waves in a laser system can be greatly extended through one such algorithm. Issues regarding practical implementation of the approach are discussed.