Dynamic Analysis About Allee Effect In A Predator-Preymodel With More Time Delay

In this paper， a predator-prey model with Allee effect and Holling type IIIfunctional response is considered from two sides： without time delay and with twotime delays respectively．The model has been made a responable extension andimprovement based on the corresponding model in the recent literature.．For the model without time delay，the existence conditions of equilibrium point，thelocal stability of equilibrium in this model and the existence of Hopfbifurcations are studied． Under two time delays，the local stability of a positiveequilibrium in system is also studied by constructing Lyapunov functionals．Theresearch shows that the positive equilibrium point will transfer to unstable fromstable and generate Hopf branch when the delay exceeds the certain critical value．...