Creating localized periodic structures with spatially localized perturbations within a defect chaotic state

In past attempts to control spatio-temporal chaos, spatially extended systems were subjected to protocols that perturbed them as a whole, often overlooking the potential stabilizing interaction between adjacent regions. We have shown that selectively applying a time-delayed feedback scheme to a specific region of a system can generate periodic patterns that are distinct form those observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. Specifically, we use spatially localized time-delayed feedback on the one-dimensional complex Ginzburg-Landau equation and demonstrate, through the numerical integration of the resulting real and imaginary equations the stabilization of novel periodic patterns within a defect chaotic regime. The mechanism underlying the observed pattern generation is related to the interplay between diffusion across the interfaces separating the different regions and time delayed feedback.