Stationary distribution and extinction of a stochastic nutrient-phytoplankton-zooplankton model with cell size

In this paper, we study a stochastic nutrient-phytoplankton-zooplankton model with cell size that represents the interaction between internal mechanism of species and external environment. We first investigate the existence and uniqueness of the global positive solution with positive initial values. Then we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solution. Once more, we find that large noise intensities cause the extinctions of phytoplankton and zooplankton. Finally, numerical simulations are given to verify the correctness of theoretical results.