| In this talk I will show the effects of a time-delayed feedback control on the appearance and development of spatio-temporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from tavelling waves. In the case of spatio-temporal chaos, the control can either stabilize uniform steady states or lead to bistability between a trivial steady state and a propagating travelling wave. Furthermore, when the basic state is a stable travelling pulse, the control is able to advance stationary Turing patterns, or yield the above-mentioned bistability regime. In each case, the stability boundary is found in the parameter space of the control strength and the time delay, and numerical simulations suggest that diagonal control fails to stabilize spatio-temporal chaos. |
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