Efficiency of the control of coexisting attractors by harmonic modulation applied in different ways

We demonstrate the destruction of attractors in the logistic map with time delayed feedback by means of a weak harmonic modulation applied in different ways. The ability of the method to select a desired state is illustrated through codimensional-two bifurcation diagrams in the parameter space of the frequency and amplitude of the control modulation. We compare the efficiencies of different kinds of the open-loop control in annihilating attractors, in particular, when the modulation is applied to a feedback variable, feedback strength or multiplicative parameter. The comparative analysis shows that modulation of the parameter is the most efficient way for destroying the attractors.