University of M, Germany

We are interested in the stability of localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of oscillons, soliton rings, labyrinth patterns or moving structures. We provide a bifurcation analysis of the delayed system and derive a system of order parameter equations for the position of the localized structure as well as for its shape. In a special case, a normal form of the delay-induced drift-bifurcation is obtained, showing that spontaneous motion extcolor{blue}{to the lowest order} arises without change of shape.