Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation

In this letter, scheme is proposed to suppress the spiral wave and multi-spiral waves in the complex Ginzburg–Landau equation (CGLE) under a local feedback control, which the perturbation is imposed on a small square area about 3×3 grids in the center of the media under periodical boundary conditions and 5×5 grids in the boundary of the media under no-flux conditions. Starting from random and/or perpendicular-gradient initial conditions, and the periodical boundary condition and/or no-flux boundary condition is in consideration, respectively. The numerical simulation results show that a target wave appears as the feedback began to work and the spiral and multi-spiral waves are overcome by the new generated target wave, furthermore, it confirms its effectiveness even if the spatiotemporal noise is introduced into the whole media.