Complete global analysis of a diffusive NPZ model with age structure in zooplankton

Abstract

Considering planktonic ecosystem as the bottom trophic levels of aquatic food webs, we derive a nutrient–phytoplankton–zooplankton model with spatially averaged parameters, where zooplankton population with two age classes and a fixed maturation period lives in a spatially bounded environment. The model can be transformed into a reaction–diffusion equation with non-local delay. Such transformation allows us to use results readily available from comparison argument and persistence theory to study the global compact attractor of solution semiflow, global attractivity and globally asymptotical stability of steady states. Our results can be used to design the control strategy of harmful algal blooms which have caused large fish kills and millions of dollars in economic losses.