The effects of toxin-producing phytoplankton and environmental fluctuations on the planktonic blooms

Abstract

Toxin-producing phytoplankton (TPP) and environmental fluctuations are important factors influencing the real aquatic ecosystems. Whether planktonic blooms are related to these factors is an interesting problem. In this paper, based on bottom-up mechanism, we first propose a nutrient–phytoplankton (NP) model with TPP under environmental fluctuations and study the extinction and persistence in mean. We also investigate the existence of ergodic stationary distribution. Taking into account seasonal variation, then we extend the NP model into a non-autonomous stochastic model and investigate the existence of periodic solution. Combined with the published data, we numerically illustrate the obtained results. From theoretical analysis and numerical simulations, periodic oscillatory succession of planktonic blooms can be seen clearly, which suggests that toxin-producing phytoplankton and environmental fluctuations play a key role in the termination of algal blooms.