Excitable dynamics and coral reef formation: A simple model of macro-scale structure development

We propose and analyze a mathematical model for coral reef dynamics at the reef scale, capturing key aspects of their long-term evolution over centuries. The model integrates fundamental ecological and physical mechanisms and exhibits excitable behavior, giving rise to diverse dynamical regimes such as traveling pulses and waves. Although these mechanisms have been independently studied, they have not been previously unified into a single framework.

The resulting self-organized spatial structures resemble real reef formations and emerge naturally, without invoking classical pattern formation mechanisms like the Turing scenario.

For tractability, we analyze a one-dimensional version of the model, assuming that the full two-dimensional system exhibits azimuthal symmetry and front stability—an assumption supported by preliminary simulations. This reduction enables a detailed bifurcation analysis based on ecologically relevant parameters, offering insights into the mechanisms underlying reef formation.