A reaction-diffusion system and its shadow system describing harmful algal blooms

Abstract

The occurrence of harmful algal blooms (HAB) in ecosystems is a worldwide environmental issue that currently needs to be addressed. An attempt to theoretically understand the mechanism behind the formation of HAB has led to the proposal of a reaction-diffusion model of the Lotka--Volterra type. In particular, a shadow system, as a limiting system of the model in which the diffusion rate tends to infinity, has been proposed to study whether or not stable nonconstant equilibrium solutions of the system exist, because these solutions are mathematically associated with HAB. In this paper, we discuss the convergence property between solutions of the full system and its shadow system from the point of view of an evolutional problem.