Wave propagation and suppression in excitable media with holes and external forcing

The propagation and suppression of spiral waves in inhomogeneous excitable media is studied numerically. The inhomogeneities correspond to either holes whose size and location are varied or constant external forcing on the activatorʹs reaction rate. For the case of a single hole and localized external forcing, it is found that the spiral wave is robust, although it may break up into two branches which reconnect with each other after the wave overcomes either the hole or the region where the external forcing is applied. When five holes are presented but there is no external forcing or the external forcing is localized, the spiral wave is robust and exhibits high concentration of the activator between holes and corners when it approaches and interacts with the holes. In the presence of several holes and external forcing across the excitable medium, the spiral wave is suppressed and the activator exhibits a breathing behaviour characterized by fronts that propagate towards the boundaries of the excitable medium, and complex patterns when the front is located near the holes.