Creating novel patterns with spatially localized perturbations in non-linear reaction-diffusion systems

In past attempts to control spatio-temporal transient chaos, spatially extended systems were subjected to protocols that perturbed them as a whole and stabilized globally a new dynamic regime, as for example a uniform steady state. We have shown that selectively applying a time-delayed feedback scheme to only part of a system can generate novel space-time patterns that are not 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 Gray-Scott reaction-diffusion system and demonstrate, through the numerical integration of the resulting kinetic equations, the stabilization of novel spatially localized periodic and quasi-periodic space-time patterns. The mechanism underlying the observed pattern generation is related to diffusion across the interfaces separating the different regions.