Dynamics of a stochastic three-species nutrient-phytoplankton-zooplankton model

Abstract

We investigate a stochastic three-species nutrient-phytoplankton-zooplankton model in this paper. We verify that the system admits a unique positive global solution starting from any positive initial value firstly. Then the sufficient conditions that guarantee the population extinction and persistence in the mean are derived. The results show that weaker white noise will strengthen the stability of the system, while stronger white noise will result in extinction of population. We also show that around the positive equilibrium point of deterministic system, the stochastic system is weakly persistent in the mean under some conditions.