Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects

Abstract: In this paper, we investigate a discrete-time phytoplankton-zooplankton model that incorporates a linear predator functional response alongside a Holling-type toxin distribution. Both Holling type II and type III cases are considered, and we derive conditions on the model parameters that guarantee the existence of positive fixed points. We classify all fixed points and analyze their global stability. Furthermore, we establish the occurrence of a Neimark-Sacker bifurcation at the positive fixed point. Theoretical results are supported by numerical simulations, which illustrate the dynamic behavior of the system