Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model

Figure 2

Phase portraits of model (1) with the parameters 𝑎₁=2, 𝑎₂=0.5, 𝑏=1, 𝑐₁=𝑐₂=2, 𝑘₁=0.4, and 𝑘₂=2.1. In this case, 𝐸₁=(0,0) is a nodal source point; 𝐸₂=(2,0) is a saddle point; 𝐸₃=(0,0.525) is a nodal sink point, which is locally asymptotically stable; 𝐸₊=(0.7791,0.7197) is a spiral sink, which is locally asymptotically stable; and 𝐸₋=(0.3208,0.6052) is a saddle point. There exists a separatrix curve determined by the stable manifold of 𝐸₋. The dashed curve is the 𝐻-nullcline 𝐻(𝑎₁−𝑏𝐻)−𝑐₁𝐻𝑃/(𝑘₁+𝐻), and the dotted curve is the 𝑃-nullcline 𝑃(𝑎₂−𝑐₂𝑃/(𝑘₂+𝐻)).