Suppression of spiral wave and turbulence by using amplitude restriction of variable in a local square area

Abstract

In this paper, a new scheme is proposed to eliminate the useless spiral wave and turbulence in the excitable media. The activator amplitudes of few sites in the media are sampled and restricted within the appropriate thresholds. At first, the local control is imposed on the center of the media, and then the local control is introduced into the left border in the media. The numerical simulation results confirm that the whole media can reach homogeneous within few time units even if the spatiotemporal noise is imposed on the whole media. To check the model independence of this scheme, the scheme is used to remove the spiral wave in the Fitzhugh–Nagumo model firstly. In our numerical simulation, the whole system is discretized into 400 × 400 sites. Then the scheme is used to eliminate the stable rotating spiral wave, meandering spiral and spiral turbulence in the modified Fitzhugh–Nagumo model, respectively. Finally, this scheme is used to remove the stable rotating spiral wave in the Belousov–Zhabotinsky (BZ) reaction. All the results just confirm its effectiveness to eliminate the spiral wave and turbulence. The criterion for thresholds selection is also discussed in the end of this paper.