Spatiotemporal complexity of the nutrient-phytoplankton model

Abstract

We consider the mathematical formulation, analysis, and numerical solution of a nonlinear system of nutrient-phytoplankton, which consists of a series of reaction-advection-diffusion equations. We derive the critical conditions for Turing instability without an advection term and define the range of Turing instability with the change of nutrient concentration. We show that horizontal movement of phytoplankton could influence the system and that it is unstable when the horizontal velocity exceeds a critical value. We also compare reaction-diffusion equations with reaction-advection-diffusion equations through simulations, with spotted, banded, and crenulate patterns produced from our model. We found that different spatial constructions could occur, impacted by the diffusion and sinking of nutrients and phytoplankton. The new model may help us better understand the dynamics of an aquatic community.