Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response

Figure 1

Diagram of positive equilibrium. (a) When 𝛼≥1/27, there exists only one positive equilibrium for any 𝛽>0. Here, 𝛼=1/27, and 𝛽=8/27. (b) When 0<𝛼<1/27, there are three cases: (i) only one positive equilibrium for 𝛽<𝛽₁ or 𝛽>𝛽₂, (ii) two positive equilibria for 𝛽=𝛽₁ or 𝛽=𝛽₂, and (iii) three positive equilibria for 𝛽₁<𝛽<𝛽₂. Here, 𝛼=1/40,  𝛽₁=0.2599, and 𝛽₂=0.2782.

(a)

(b)