Dynamical Analysis of a Nitrogen-Phosphorus-Phytoplankton Model

Abstract

This paper presents a nitrogen-phosphorus-phytoplankton model in a water ecosystem. The main aim of this research is to analyze the global system dynamics and to study the existence and stability of equilibria. It is shown that the phytoplankton-eradication equilibrium is globally asymptotically stable if the input nitrogen concentration is less than a certain threshold. However, the coexistence equilibrium is globally asymptotically stable as long as it exists. The system is uniformly persistent within threshold values of certain key parameters. Finally, to verify the results, numerical simulations are provided.

Dynamics Induced by Delay in a Nutrient‐Phytoplankton Model with Multiple Delays

“…In the absence of delay, theoretical analysis indicated that the unique positive equilibrium is globally asymptotically stable in model (1) if it exists. Deng et al [48] also studied a nitrogen-phosphorus-phytoplankton model without delay, where Holling II function was employed to describe the nutrient uptake dynamics of phytoplankton. Although the function modelling the nutrient uptake dynamics of phytoplankton is different, they get the same results.…”