Dynamical Analysis Of A Predator-Prey Model With The Allee Effect And Constant-Yield Prey Harvesting

The dynamical behaviors of a Leslie-Gower predator-prey model with both strong Allee effect and constant-yield prey harvesting are analyzed in this paper.To begin with,the existence,type and stability of the equilibrium point under the influence of Allee effect and constant harvesting are analyzed by qualitative theory.It is showed that there are multiple types of equilibrium points when the parameters meet different conditions.In particular,The system has a cusp of codimension at least 3 when the parameters are under certain conditions,and the existence of the cusp of codimension 3 is proved.Secondly,the bifurcations of the system are analyzed under the different parameters.As the change of parameters,the saddle-node bifurcation,subcritical Hopf bifurcation and supercritical Hopf bifurcation,the Bogdanov-Takens bifurcations of codimensions 2 and 3 are shown in the system by the bifurcation theory.Therefore,the system has limit cycles and homoclinic loops if appropriate parameters are selected.Finally,according to the parameter conditions,the model was numerically simulated with different parameters to obtain the phase diagram analysis that near the equilibrium point.