Abstract
<title>Abstract</title> <p>Coral reefs are among the most vital ecosystems on the planet, sustaining exceptionally high biodiversity and providing essential ecological services to coastal communities. However, coral populations have been steadily declining for decades, primarily due to stressors such as rising ocean temperatures and disruptions in the global carbon cycle. Mounting evidence suggests that coral reefs are rapidly approaching ecological tipping points, where even small increases in atmospheric carbon could trigger catastrophic shifts in ecosystem functioning and long-term stability. In this work, we develop and analyze a system of coupled nonlinear differential equations representing the dynamics of carbon concentration, global average ocean temperature, and coral populations. Through a combination of rigorous mathematical techniques and computational simulations, we investigate the tipping mechanism within this system. Our analysis uncovers a rich set of dynamical features, including bifurcations, critical transitions, and prolonged transient states. Importantly, some of these transitions culminate in coral extinction scenarios, while others reveal conditions under which reefs may persist or recover. A deep learning model has been applied to detect bifurcation using simulated coral reef data. These findings underscore the pressing need to comprehend the interplay between carbon emissions, climate forcing, and biological processes in shaping reef survival.</p>