Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms

• Develop a new spatial–temporal planktonic model.
• A Hopf bifurcation occurs as the delays increase through a certain threshold.
• Harvest effort can change the equilibrium point and stability of the system.
• Diffusion can affect the stability of the system.

In this paper, we study the dynamics of a bioeconomic plankton model with delay and diffusion terms, in which phytoplankton is assumed to undergo exploitation. Some sufficient conditions ensuring the stability and bifurcation for the model are provided by using stability and bifurcation theory. Our results show that harvest effort can control bifurcation and resume system’s stability in the case of positive economic profit, and over exploitation will result in the extinction of the population which is in line with reality. Finally, some numerical simulations are given to verify the analytical results of nutrient–phytoplankton–zooplankton–fish model.