Investigation of branching structure formation by solutions of a mathematical model of pattern formation in coral reefs

A reaction-diffusion type mathematical model for the growth of corals in a tank, describing the spatial time evolution of the biomass of dissolved nutrients (food of polyps) and dissolved solid materials (calcium carbonate) of the tank, is considered. Some properties of the spatial patterns when the model parameters lie in the Turing space are investigated based on dispersion relation and unstable wave numbers of the linearised system. Branching structure formation process in the model is explained analytically. The model is solved numerically in one dimension subject to no-flux boundary conditions and it is shown that the numerical results agree with the analytically derived properties of the solutions.