Domain of attraction for stabilized orbits in time delayed feedback controlled Duffing systems

Time delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, this control method still has an open problem of estimating domain of attraction for target unstable periodic orbits. In this paper, we numerically discuss the domain of attraction in Duffing systems under the control method. The disturbance to initial conditions reveals that the domain of attraction possibly exhibits self-similar structures in its boundaries.