Topological singularities of domains in globally constrained bistable reaction-diffusion systems

A general (nonvariational) globally constrained reaction-diffusion equation (GCRDE) with bistability is employed for studying the dynamics of two-dimensional non-single-connected domains: circular spots of one phase with inclusions of another phase. In the sharp-interface approximation, the dynamics is describable by a set of coupled ordinary differential equations which have a universal form. It is shown that domains with a single inclusion always develop topological singularity in a finite time: the inclusion either shrinks to zero, or breaks out. The results are supported by numerical simulations with the full GCRDE.