Moment Dynamics for Toxic-Phytoplankton–Zooplankton Systems with Environmental Noises

In this paper, we propose and study two different forms of toxin-producing phytoplankton–zooplankton models under the influence of environmental noises in two ways: one is to use Gaussian white noise to disturb the growth rate of phytoplankton and the mortality rate of zooplankton, the other is to make white noise disturb the intrinsic growth rate of the two populations by introducing multiplicative noise term. We derive the differential equations of first and second moments by using statistical linearization technique, and then study the stability of the moment differential equations with the help of the Routh–Hurwitz criterion. We also discuss the effect of environmental noise on the second moments of the stochastic models.