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

Figure 8

The trajectory graphs and phase portrait of system (7) without delay for (𝛼,𝛽)∈𝐷₃ with 𝛼=0.01 and 𝛽=0.24. (a)-(b) 𝛾=0.1<min{𝛾₀₁,𝛾₀₃}. The initial value is (0.626,0.15). All of the three equilibria are unstable and there exists a stable periodic orbit. (c)-(d) 𝛾₀₃<𝛾=0.3<𝛾₀₁. The initial value is (0.049,0.0116). The positive equilibria 𝐸^∗₁ and 𝐸^∗₂ are unstable and the positive equilibrium 𝐸^∗₃ is stable.

(a)

(b)

(c)

(d)