Spot-splitting dynamics on a sphere

About the model The Schnakenberg model is one of the standard reaction-difusion systems, and depending on the parameter set various types of solutions can be obtained. On the video we are examining the effect that domain growth has on a stable spot solution. We start with a one spot stable solution that destabilizes and breaks into 3 spots, with five more generated on lower on the sphere. As time advances the spots distribute equidistantly from each other. We used the closest point method for solving the differential equation. It's a very intuituve and easy to use extension of finite differences that works on any domain. Special thanks to Steve Ruuth for all the help.

Some references Steve Ruuth's website Colin Macdonald's page on the CPM