Dynamic behavior analysis of phytoplankton-zooplankton system with cell size and time delay

This paper focuses on the dynamic behavior of phytoplankton-zooplankton system with cell size and time delay. Remarkably, the existence of cell size and time delay make the dynamic behavior of the system more close to the real-world situation, essentially different from those in the existing related literature. To analyze the dynamic behavior of the system, the positiveness and boundedness of the solution are first derived. Then, the asymptotic stability of the coexistent equilibrium and Hopf bifurcation are studied by analyzing the associated characteristic equation. Once more, the direction of Hopf bifurcation and the stability of bifurcated periodic solution are determined. Finally, the theoretical results are illustrated by a numerical example.