Pattern Dynamics of a Diffusive Toxin Producing Phytoplankton–Zooplankton Model with Three-Dimensional Patch

Abstract

In this paper, the Turing pattern formation in a diffusive toxin producing phytoplankton–zooplankton model with three-dimensional patch is investigated. Firstly, the conditions for the existence of Hopf bifurcation and stationary pattern are obtained based on the linear stability analysis. Then, the amplitude equations are derived by using nonlinear analysis and standard multiple-time-scale analysis. This study shows that there exists a pattern transition from spot pattern to stripe pattern with the decrease of the amount of toxicity, and the death rate of zooplankton also has a significant effect on the pattern structure. The obtained results suggest that the toxicity of phytoplankton and the death rate of zooplankton both play vital roles in the spatial distribution of population density.