Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect

Figure 1

The phase portrait of model (7) with the strong Allee effect. The parameters are taken as 𝑎=0.25, 𝛿=0.8, 𝑚=1.3 and 𝑟=0.15. In this case, 𝐸₀=(0.3,0) is an unstable node point, 𝐸₁=(1,0) and 𝐸₋=(0.5,0.4) are saddle points; the positive equilibrium 𝐸₊=(0.6,0.48) is local asymptotically stable. There exists a separatrix curve determined by the stable manifold of the equilibrium point 𝐸₋. The dotted curves are the nullclines.