The impact of acid-base changes on the stochastic dynamics of phytoplankton growth under global warming

This paper deals with a stochastic nutrient-phytoplankton (NP) model with the impacts of pH and global warming, where the stochastic environmental disturbance is characterized by the logarithmic Ornstein-Uhlenbeck (LOU) process. In the deterministic NP model, we investigate the existence of possible equilibria and analyze their local and global stability. Additionally, by utilizing sensitivity analysis technique, it is shown that phytoplankton density and nutrient concentration are highly sensitive to global warming and pH. In the stochastic NP model, we derive the sufficient conditions of exponential extinction and persistence in the mean of phytoplankton, prove the existence of a stationary distribution, and give the specific expression of the probability density under some appropriate conditions. Ecologically, via numerical simulations, we find that the variation in global warming and pH can generate new influence mechanisms for the interactions between nutrient and phytoplankton within the deterministic and stochastic environments. One of the most interesting results is that an appropriate increase or decrease in pH value is beneficial for inhibiting the occurrence of phytoplankton blooms. This study may provide some new ideas for understanding the dynamic mechanisms of phytoplankton growth in natural aquatic environments.