How bifurcation theory explains coral reef formation

In this talk, I will explore the change in the behavior of the solutions within a model for coral reef formation. This model effectively replicates the macroscopic structures of coral reefs through interactions at a mesoscopic scale. By applying certain simplifications, I derived a streamlined version of the original model that is amenable to mathematical analysis while retaining sufficient complexity to exhibit diverse dynamical changes across the parameter space. The findings from this study have significant ecological implications, enhancing the model's descriptive power.