Bifurcation analysis in a diffusive phytoplankton–zooplankton model with harvesting

Abstract A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the as parameter, we get existence and stability of positive steady state, also investigate spatially homogeneous inhomogeneous periodic solutions. Then, by applying normal form theory center manifold theorem, give direction Hopf bifurcation from state. In addition, prove Bogdanov–Takens bifurcation. These results reveal that diffusion really affect spatiotemporal complexity system. Finally, numerical simulations are given to support our theoretical analysis.