Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays

We take the delays due to gestation of two kinds of zooplankton as parameters, the dynamics of a two zooplankton-phytoplankton model is studied, we discussed the dynamics under six conditions: (1) τ1=τ2=0,(2) τ1>0,τ2=0, (3) τ1=0,τ2>0, (4) τ1=τ2>0, (5) τ1 ∈ (0, τ10), τ2 > 0, (6) τ2 ∈ (0, τ20), τ1 > 0, the Hopf bifurcation about condition (5) should be studied by center manifold theorem and normal form. At last, some simulations are given to support our results