Joint impact of global warming and Allee effect on the phytoplankton–zooplankton dynamics under the mean-reverting Ornstein–Uhlenbeck process

This work investigates the dynamics of a phytoplankton–zooplankton (PZ) model with global warming and Allee effect, as well as its stochastic version, where stochastic environmental disturbance is characterized by the mean-reverting Ornstein–Uhlenbeck process. In the deterministic PZ model, we numerically and theoretically study the dynamics of stability and Hopf bifurcation. Our results reveal that the weakened global warming can eliminate the bistable phenomenon caused by the Allee effect, while the reduced Allee effect cannot affect the bistable phenomenon caused by global warming. Furthermore, despite that the intensification of global warming cannot change the bistable phenomenon caused by the Allee effect, it can alter the type of bistable. In the stochastic PZ model, we mainly study the existence of stationary distribution, the probability density function, and survival dynamics of plankton, which in turn provides a theoretical basis for numerical simulations. Numerical analysis shows that the intensity of volatility, the speed of reversion, and the variations of global warming and Allee effect can regulate the skewness of stationary distribution for plankton. The numerical results are in good agreement with the theoretical findings.