Highlights
- It is established that a new a stochastic coral-starfish model with global warming and ocean acidification.
- It is revealed that the change in global warming has a decisive impact on the dominant position of corals and starfish.
- It is found that the variation of pH is able to destabilize coral-starfish interactions.
Abstract
The intensification of global warming and ocean acidification are important factors affecting coral reef degradation, however, their impact mechanisms on coral reef system are still unclear. In this paper, we study the dynamics of a stochastic coral-starfish model considering the factors of global warming and ocean acidification, where the stochastic environmental fluctuation is characterized by mean-reverting Ornstein-Uhlenbeck (OU) process. A key advantage of considering global warming and ocean acidification in coral reef systems is that it can accurately describe the dynamic mechanisms of coral-starfish interactions, providing a scientifically reliable theoretical basis for exploring the evolutionary succession of coral reef systems. The main purpose of this paper is to investigate how global warming and ocean acidification affect the dynamic mechanisms of coral reef systems in the presence and absence of stochastic disturbances. Mathematically, we mainly study the critical threshold conditions for the transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation of deterministic coral reef system, as well as the existence of ergodic stationary distribution, precise expressions of probability density function, persistent in the mean, and stochastic extinction dynamics in stochastic coral reef system, which in turn provide a theoretical basis for numerical simulations. Numerical analysis indicates that the variations of global warming and ocean acidification can generate a great influence on the coral-starfish dynamics with and without OU process. Significantly, it is found that coral growth dominates under the increasing global warming effect, while starfish growth dominates under the decreasing global warming effect in a randomly perturbed environment. Furthermore, the change of pH has capacity to destabilize coral-starfish interactions, while the intensified global warming can lead to the extinction of starfish. These findings may contribute to the studies of potential strategies for protecting coral reef ecosystems under the impact of climate change.
Liao T. & Chen J., in press. Dynamics of a coral reef system under climate change. Chinese Journal of Physics. Article (restricted access).
