The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching

Abstract

This paper addresses a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching. The stochastic model in this paper includes white and colored noises. For the model, we first prove the existence of the global positive solution of the model. And then by using Khasminskii’s method and Lyapunov function, we derive sufficient conditions for the existence of a unique ergodic stationary distribution. Finally, numerical simulations are carried out to support our results.