Adaptive time-delayed feedback control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback parameters, using the speed-gradient method of control theory. For a delay-coupled network of Stuart-Landau oscillators (normal form of supercritical Hopf bifurcation) we show that by adaptively tuning the coupling phase, as well as the coupling strength and the delay time, one can easily control the stability of different synchronous periodic states, namely in-phase, cluster, or splay states. Our results are robust even for slightly nonidentical elements of the network