Threshold dynamics of a diffusive nonlocal phytoplankton model with age structure

Abstract

In this paper, a reaction–diffusion equation with age structure and nonlocal effect for the maturation, growth and spatial distribution of phytoplankton in a water column is derived, and the threshold dynamics for the model is completely classified. It is shown that the death rate and maturation time of the phytoplankton both affect the dynamics of the model. The phytoplankton species could die out if the death rate is greater than a critical death rate. However, when the death rate is less than the critical value, there exists another threshold for the maturation period such that the unique positive steady state (respectively, the trivial steady state) is globally attractive if the maturation period is less (respectively, greater) than the threshold value.