Spiral waves in systems with fractal heterogeneity

•We consider a heterogeneous area in an excitable medium with a fractal shape.•The fractal heterogeneity does not lead to the suppression or breakup of the spiral wave.•Different levels of heterogeneity can induce fruitful transitions of the spiral tip trajectory.•The spiral tip will be a stable rotating type for strong heterogeneity, whatever transitions have been induced by weak heterogeneity.

The influence of fractal heterogeneity on a spiral wave in an excitable system is numerically studied based on the Barkley model. The heterogeneity is implemented by letting the diffusive coefficient in the heterogeneous area be different from the other area. The results show that fruitful transitions of the spiral tip trajectories are induced by the fractal heterogeneity. In particular, when the heterogeneity increases to a sufficiently high level the spiral tip trajectory always changes to a stable rotating trajectory (closed-circle tip trajectory), whatever transitions have been induced by a lower level of heterogeneity. We qualitatively ascribe the transitions to the attraction on the spiral tip exerted by the heterogeneous area.