In this study, we present a novel model that successfully replicates the observed formations of coral reefs. Our proposed model is based on partial differential equations and incorporates the wealth of knowledge accumulated over the past decades regarding the physical and ecological interactions occurring at the micro- and mesoscales within these systems. These interactions include clonal growth, facilitation, the uptake of resources by corals, and the supply of these resources by ocean water currents, among others. Through the mathematical analysis of this model using bifurcations theory, we uncover that the interplay of only a few parameters of the model is sufficient to elucidate the emergence of various reef shapes found in nature. This includes the formation of fringing reefs, closed atolls, and the inner structures within closed atolls. Our findings provide valuable insights into the underlying mechanisms driving the diverse morphologies observed in coral reefs.
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