Delayed feedback induces motion of localized spots in reaction-diffusion systems
Mustapha Tlidi, Alberto Sonnino, and Giorgio Sonnino
Accepted
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 an hysteresis loop. We show that the space time dynamics of the FitzHugh-Nagumo in the vicinity of that critical point, could be described by the delayed Swift-Hoheneberg equation. We show that the delay 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. PACS numbers: 82.40.Ck, 82.40.Bj, 89.75.Fb, 47.54.Fj