Asymptotic Behavior of a Stochastic Generalized Nutrient–Phytoplankton–Zooplankton Model

In this paper, we consider the stochastic nutrient–phytoplankton–zooplankton model with nutrient cycle. In order to take stochastic fluctuations into account, we add the stochastic increments to the variations of biomass of nutrition, phytoplankton and zooplankton during time interval \(\Delta t\), thus we obtain the corresponding stochastic model. Subsequently, we explore the existence, uniqueness and stochastically ultimate boundness of global positive solution. By constructing suitable Lyapunov function, we also obtain V-geometric ergodicity of this model. In addition, the sufficient conditions of exponential extinction and persistence in the mean of plankton are established. At last, we present some numerical simulations to validate theoretical results and analyze the impacts of some important parameters.