Bifurcation Analysis In A Predator-prey Model With Allee Effect

In this paper,the effect of Allee effect on Lesile-Gower type predator-prey system with predator harvesting is studied.We analyze the existence of equilibrium point and some bifurcation phenomena.For some specific parameter values of this model,the codimension of Bogdanov-Takens singularity（cusp type）is 3.Compared with the general Holling I type predator-prey model,the system has rich dynamic behaviors and high codimension degenerate branches.It is shown that vary with parameters,the system can exhibit saddle-node bifurcation,Hopf bifurcation,attracting and repelling BogdanovTakens bifurcation with codimension 2 and 3.The rationality of the results is verified by numerical simulation.