Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling. (November 2019) - Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua
Abstract: To investigate the effects of stochasticity and seasonality on the dynamics of aquatic ecosystems, in this paper, we propose two stochastic nutrient-plankton food chain models. For the stochastic model with regime switching, we establish sufficient conditions for the persistence and extinction of plankton. Under mild extra assumptions, the existence of an ergodic stationary distribution is studied. For the stochastic model with seasonal fluctuation, we first perform the survival analysis. Then, based on Khasminskii's theory for periodic Markov processes, we give sufficient criteria for the existence of a positive stochastic periodic solution. Numerical simulations are carried out to illustrate the analytical results, showing that stochasticity and seasonality may cause the periodic bloom of phytoplankton, which partly explains the formation of algal blooms.