Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion

In the limit of a large duffusivity ratio, spotlike solutions in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are studied. It is shown analytically that such spots undergo an instability as the diffusivity ratio is decreased. An instability threshold is derived. For spots of small radius, it is shown that this instability leads to a spot splitting into precisely two spots. For larger spots, it leads to deformation, fingering patterns, and space-filling curves. Numerical simulations are shown to be in close agreement with the analytical predictions.