Coral reefs have evolved over hundreds of millions of years and are now
considered one of the most critical yet vulnerable ecosystem on earth. Environmental
changes, including variations in light availability, nutrient levels, and fishing pressure, can significantly impact the health of coral reefs, potentially leading to ecosystem degradation. A coral-macroalgae-herbivorous fish model is developed based on
ecological stoichiometry to investigate the dynamics of coral-algae phase shifts. The
positivity, invariance, and dissipativity of the model are carefully established, the existence and stability of equilibria are rigorously demonstrated, and rich dynamics such
as bistability and various types of periodic oscillations are numerically explored. Furthermore, the effects of environmental factors (e.g., light intensity, nutrient levels, and
fishing pressure) on the system’s dynamics are investigated. The main findings highlight that environmental variations are key drivers of ecological phase transitions in
coral reef ecosystems, providing more insights into the mechanisms underlying coral-algae dynamics and offering implications for the sustainable management of coral
reefs.