Dynamical Properties of a Nutrient‐Phytoplankton‐Zooplankton Model Incorporating Ornstein–Uhlenbeck Process

In this paper, a stochastic nutrient‐phytoplankton‐zooplankton (NPZ) aquatic model with the inevitable effects of environmental perturbations is our research focus. The maximum specific ingestion rate of phytoplankton and predation coefficient of zooplankton follow log‐normal Ornstein–Uhlenbeck (OU) process. The deterministic model confirms the existence and local asymptotic stability of equilibria. To demonstrate the dynamic behavior of the stochastic model, we first verify the existence of the global positive solution. Then, by virtue of suitable Lyapunov functions, we establish sufficient conditions for extinction and the existence of a stationary distribution, which indicates whether plankton can survive persistently or not. Next, we obtain the probability density function around the positive equilibrium point of the corresponding deterministic model, which is a local Gaussian‐type approximation derived from the linearized system and reflects the persistence of plankton in water ecosystems. Finally, we present some numerical simulations to illustrate the theoretical results. Besides, our findings indicate that high volatility intensity can expedite the extinction of the plankton, while low volatility intensity can ensure that plankton reach a stationary distribution. This conclusion may be useful in developing strategies for algal bloom prevention and water quality control.