Wave propagation in heterogeneous excitable media

Heterogeneities deeply affect pulse dynamics in excitable media. In one dimension, spatially periodic variation of the excitation threshold leads to a characteristic dependence of the propagation speed on the modulation period $d$ with a maximum at a certain optimal value $d_{\mathrm{opt}}.$ The maximum speed may be larger than the pulse velocity in an effective homogeneous medium. In two dimensions, the geometry and size of heterogeneities determine the wave dynamics. For example, an excitability distribution made of oblique stripes with different angles of inclination can result in a speedup or a slowdown of the pulse. The calculations are carried out with a modified Oregonator model for light-sensitive Belouzov-Zhabotinskii media where a heterogeneous distribution of excitability can be achieved by inhomogeneous illumination. Nevertheless, the results do not depend on the details of the local kinetics, but apply to the general case of excitable media.