Bifurcation analysis of modified Leslie-Gower predator-prey model with double Allee effect

Abstract

In the present article, a modified Leslie-Gower predator-prey model with double Allee effect, affecting the prey population, is proposed and analyzed. We have considered both strong and weak Allee effects separately. The equilibrium points of the system and their local stability have been studied. It is shown that the dynamics of the system are highly dependent upon the initial conditions. The local bifurcations (Hopf, saddle-node, Bogdanov-Takens) have been investigated by considering sufficient parameter(s) as the bifurcation parameter(s). The local existence of the limit cycle emerging through Hopf bifurcation and its stability is studied by means of the first Lyapunov coefficient. The numerical simulations have been done in support of the analytical findings. The result shows the emergence of homoclinic loop. The possible phase portraits and parametric diagrams have been depicted. © 2016 Ain Shams University