Stochastic periodic solution of a nutrient-plankton model with seasonal fluctuation

In this paper, a stochastic nutrient-plankton model with seasonal fluctuation was developed to investigate how seasonality and environmental noise affect the dynamics of aquatic ecosystems. First, the survival analysis of plankton was proposed. Then, by using Lyapunov function and Khasminskii's theory for periodic Markov processes, we derive the sufficient conditions for the existence of positive periodic solution. The numerical simulations were carried out to provide a better understanding of the model, and the results indicate that seasonal fluctuation is beneficial to the coexistence of plankton species.