一类具有饱和迁移率的时滞捕食-食饵生物控制模型

In this paper, we establish a delayed predator prey model with saturation predator migration rate and analyze global dynamical behavior of this model. Because of the delay effectof predations on the variation of predator's biomass, this model is formulated as a system of delayed differentialequations. The existence and stability of equilibria are studied. Sufficient conditions areobtained which ensures that Hopf bifurcation occurs when the delay is regarded as a bifurcationparameter. By applying the center manifold theorem and normal form theory, computational formula are derived for the direction and stability of Hopf bifurcating periodic solutions. Some numerical simulations illustratethe theoretical results.