Dynamics of a Diffusive Nutrient-Phytoplankton-Zooplankton Model with Spatio-temporal Delay

Abstract

We study a diffusive nutrient-phytoplankton-zooplankton (NPZ) model with spatio-temporal delay. The closed nature of the system allows the formulation of a conservation law of biomass that governs the ecosystem. We advance the understanding of the local stability for equilibrium solutions of the NPZ model by proposing a new local stability theorem for generalized three-dimensional systems. Using a specific delay kernel, we perform a qualitative analysis of the solutions, including existence, uniqueness, and boundedness of the solutions, global stability of the trivial equilibrium, and Hopf bifurcation of the nontrivial equilibrium. Numerical simulations are also performed to verify and supplement our analytical results. We show that diffusion predominantly has a stabilizing effect; however, if sufficient nutrient is present, complex spatio-temporal dynamics may occur.