title: Delayed feedback induces motion of localized spots in reaction-diffusion systems.
abstract: We study the formation of localized structures, often called localized spots, in reaction-diffusion systems subject to time delayed feedback control. We focus on the regime close to a second-order critical point marking the onset of a hysteresis loop. We show that the space-time dynamics of the FitzHugh-Nagumo model in the vicinity of that critical point could be described by the delayed Swift-Hohenberg equation. We show that the delayed feedback induces a spontaneous motion of localized spots. We characterize this motion by computing analytically the velocity and the threshold above which localized structures start to move in an arbitrary direction. Numerical solutions of the governing equation are in close agreement with those obtained from the delayed Swift-Hohenberg equation.
authors.affiliation: Faculté des Sciences, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium.
authors.forename: Mustapha
authors.initials: M
authors.lastname: Tlidi
authors.forename: Alberto
authors.initials: A
authors.lastname: Sonnino
authors.forename: Giorgio
authors.initials: G
authors.lastname: Sonnino