Periodic solutions of an NPZ model with periodic delay and space heterogeneity

Abstract

In this paper, we investigate a nutrient-phytoplankton-zooplankton (NPZ) model with seasonality and spatial heterogeneity, in which the immature zooplankton with size structure is described by the quasi-linear first-order partial differential equation. A three-dimensional periodic delay food chain model with initial value is derived from the original model. To establish the threshold dynamics of NPZ model, we first obtain the global attractivity of the positive periodic solution of the nutrient-phytoplankton (NP) subsystem by using the method of sub-super solutions and associated iterations. We then give the integral expression of threshold for the corresponding system, which is convenient for numerical simulations. Based on this, the threshold dynamics is discussed by appealing to the comparison arguments and the persistence theory. Finally, the analytic results are in good consistence with our numerical simulations.