Modeling the effect of ocean warming and seawater salinity on a coral reef system under the Ornstein-Uhlenbeck process
摘要
Climate change-driven coral bleaching poses a significant threat to marine biodiversity. This study investigates the dynamics of a coral reef system influenced by ocean warming and salinity fluctuations, employing both deterministic and stochastic. Environmental variability is modeled using a mean-reverting Ornstein-Uhlenbeck process—an innovative technique in coral reef studies. In the deterministic framework, we analyze boundedness of solutions, identify equilibrium points, and examine various bifurcations, including Hopf, transcritical, and saddle-node. For the stochastic model, we establish the existence of a unique global solution, demonstrate the presence of an ergodic stationary distribution, and derive the associated probability density function. The key ecological insights include persistence in the mean, conditions for stochastic extinction, and the critical role of starfish mortality in potential population collapse. Further, salinity-induced double Hopf bifurcations are observed, while lower temperature levels may help reduce system instability. The stationary distributions are notably skewed, shaped by salinity levels and environmental capacity, and an optimal range of temperature and salinity supports coral and starfish coexistence. Overall, the findings offer valuable perspectives on coral reef resilience and strategies for biodiversity conservation.