Dynamics in a diffusive phytoplankton–zooplankton system with time delay and harvesting

Abstract

The phytoplankton–zooplankton is fundamentally important to study plankton and protect marine environment. In this paper, we propose a diffusive phytoplankton–zooplankton model, in which we also consider time delay in zooplankton predation and harvesting in zooplankton. By analyzing the distribution of eigenvalues, we investigate the stability of the positive equilibrium and the existence of Hopf bifurcation using time delay as a bifurcation parameter. We analyze the property of Hopf bifurcation and give an explicit formula for determining the direction and the stability of Hopf bifurcation. Finally, by numerical simulation, we analyze the effect of harvesting, conversion rate, half-saturation, and time delay. We conclude that harvesting parameter, conversion rate, and half-saturation constant all can be used in controlling the bloom of plankton population.