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Phytoplankton is an important indicator organism to evaluate the quality of water environment, which may reflect the nutritional level of the sea area. Conversely, environmental conditions can directly affect the community structure of phytoplankton. A stochastic phytoplankton–zooplankton model considering non-degenerate and degenerate diffusions is formulated in this paper. What’s more, in both systems, we obtain sufficient conditions of extinction and ergodicity. Our results demonstrate that the weaker white noise can ensure the permanence of zooplankton and the stronger white noise can lead to the disappearance of zooplankton. Moreover, the threshold value of extinction and persistence can serve as a theoretical basis for controlling phytoplankton and zooplankton. Numerical examples are performed on the analysis results of the two cases to confirm our theoretical results. In addition, we also provide a real-life case study, the validity of the model is verified based on experimental data, and it is shown that fluctuation of external environment and the consumption of phytoplankton by zooplankton will affect the growth and number of phytoplankton. Effectively controlling the quantity of phytoplankton can delay the occurrence of water bloom or red tide. [ABSTRACT FROM AUTHOR]

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]