Control of spiral drift by using feedback signals from a circular measuring domain in oscillatory media

Abstract

In this paper, a non-local feedback is used to force spiral waves in the oscillatory system modeled by the complex Ginzburg-Landau equation, where the feedback signal is derived from a circular measuring domain. It is found that the spiral tip could be driven to follow an attractor after a period of drift. The existence of multiple types of attractors, which include a point attractor at the measuring center and a set of circular attractors concentric with the measuring domain, is illustrated. Which to be chosen depends on the direction of the spiral initial drift and the distance between the initial tip position and the measuring center. Here the diameter of the circular attractor has a periodic change with the size of the measuring domain, but is not affected by the movement of the measuring domain. Correlation between the tip drift and the feedback signal is analyzed, and the modulus function of the feedback signal will has a constant value after the spiral tip arrives at the attractors. If the feedback signal is generated from the measuring domain far away from the position of the initial spiral tip, the spiral breakup can be caused by the feedback control, and it fist occurs near the boundary and then invades inward until the area of the remaining spiral is small enough. The effect of the feedback gain, the delay time and the scaling parameter is also considered.