Control of spiral waves and spatiotemporal chaos by periodic perturbation near the boundary

In this paper, the relation between the excited period and the perturbation one is firstly studied, and several segments of linear relation can be found. Their appearance is mainly due to the existence of vulnerable periods and absolute refractory ones. Further, a method for controlling spiral waves and spatiotemporal chaos in excitable media is proposed. In the method, a target wave train is generated by periodic perturbation in a small rectangle region near the left boundary, and competes with spiral waves or spatiotemporal chaos. The availability and efficiency of the control depend on the comparison of excited periods between spiral waves or spatiotemporal chaos and target wave trains, the selection of perturbation period is tied to the relation between the excited period and the perturbation one. These results are interesting to understand many real cases, such as heart diseases and their therapy. We find spiral-wave tip can flee away from the boundary, but the elimination of the tip is very difficult. The effect of noise is also considered.