Qualitative Analysis for a Phytoplankton-Zooplankton Model with Allee Effect and Holling Type II Response

This paper investigates a predator-prey system with Allee effect and Holling type-II functional response consisting of phytoplankton as prey and zooplankton as a predator. For the non-spatial system, we analyzed the stability, the existence of Hopf bifurcation at the coexistence equilibrium and stability of bifurcating periodic solutions are obtained. Moreover, the diffusion driven instability, Hopf bifurcation of the corresponding spatial system with zero flux boundary conditions and Turing instability region regarding parameters are established. Numerical simulations are provided to illustrate theoretical results.