Qualitative Dynamics of a Discrete Phytoplankton-Zooplankton System with Holling Type II Grazing and Type III Toxin Release

We study the dynamics of a discrete phytoplankton-zooplankton model with Holling type~II grazing and Holling type~III toxin release. The existence and stability of positive fixed points are analyzed, and conditions for the occurrence of Neimark–Sacker bifurcation are established. We show how feedback control can suppress complex dynamics near bifurcation. Global stability of the boundary equilibrium is also discussed. Numerical simulations confirm the theoretical findings, illustrating the rich behavior of the model under varying parameters