Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises

Abstract

In this paper, we propose a stochastic phytoplankton–zooplankton model driven by correlated colored noises, which contains both anthropogenic and natural toxins. Using Khasminskii transformation and the stochastic averaging method, we first transform the original system into an Itô diffusion system. Afterwards, we derive the stationary probability density of the averaging amplitude equation by utilizing the corresponding Fokker–Planck–Kolmogorov equation. Then, the stability of the averaging amplitude is studied and the joint probability density of the original two-dimensional system is given. Finally, the theoretical results are verified by numerical simulations, and the effects of noise characteristics and toxins on system dynamics are further illustrated.