Abstract:
The coexistence solutions of a predator-prey model with strong Allee effect are studied. Firstly, by using local bifurcation theory and regarding the growth rate of the predator b as a bifurcation parameter, the existence of the local bifurcation branch from the semi-trivial solution branch is proved. Secondly, the local bifurcation branch can be extended to a global bifurcation branch by global bifurcation theory. The sufficient condition for the existence of coexistence solutions is got. Finally, the trend of the global bifurcation branch is depicted. It is shown that the bifurcation diagram of this model is a Loop, which indicates that coexistence solutions of the model are existed whenever b∈λ1-du*21+mu*2,λ1-du*11+mu*1, the parameter M∈0,12(which reflects the intensity of strong Allee effect), and the inherent growth rate of the prey r>r*.
