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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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of water temperature on phytoplankton–zooplankton dynamics with Holling type III functional response. Remarkably, growth rate, capture rate, handling time, death rate and Holling parameter are considered to be temperature dependent, which makes the model different from those in the existing related literatures. First, the relationships between model parameters and water temperature are presented. Then we give the positivity and boundedness of the solutions. And parameters dependent equilibrium analysis and stability analysis are obtained, respectively. It shows that when the water temperature is lower or higher than the optimal temperature, the equilibrium density of phytoplankton increases with decreasing capture rate and increasing handling time. Meanwhile, we show that the decrease of capture rate and increase of handing time cause the density of zooplankton also increases without the optimal temperature, while the population of zooplankton tends to decrease with decrease of growth rate. In addition, sensitivity of coexisting equilibrium to the parameters of the phytoplankton–zooplankton model is analyzed. Finally, one parameter bifurcation analysis is done. [ABSTRACT FROM AUTHOR]