Abstract
Although the long‐term dynamics of the prey‐predator model has analyzed in the passing decades, the threshold of extinction and persistence has not been well unified, especially the higher order perturbation affects the phytoplankton‐zooplankton dynamics. Here, we formulate a stochastic phytoplankton‐zooplankton model with nonlinear perturbation. A uniform expression of threshold value of extinction and ergodicity for this model is derived. In addition, the sufficient conditions of strong and weak persistence in the mean of phytoplankton and zooplankton are given. Our results indicate that white noise influences the dynamics of both phytoplankton and zooplankton species, which further affects the stability of phytoplankton‐zooplankton models. Some numerical examples are provided to support our theoretical results, and their explanations from the perspective of ecology are presented in this paper.