Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations

Abstract

This paper describes an analytical and numerical investigation of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton (TPP) and impulsive perturbations. White noise, impulsive perturbations, and TPP were incorporated into the system to stimulate natural aquatic ecological phenomena. The aim of this paper was to analyze how these factors affect the dynamics of the system. Mathematical derivations were utilized to investigate some key threshold conditions that ensure the existence and uniqueness of a global positive solution, population extinction, and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. The numerical results indicated that both white noise and the impulsive control parameter can directly influence population extinction and persistence in the mean. Enhancing the toxin liberation rate of TPP increases the possibility of phytoplankton survival but reduces zooplankton biomass. These results improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment.