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

Figure 7

The trajectory graphs and phase portrait of system (6) for (𝛼,𝛽)∈𝐷₂ with 𝛼=0.2,  𝛽=1.2, and 𝛾=0.06. (a)-(b) For 𝜏=0.04<𝜏₀, the positive equilibrium 𝐸^∗ is stable. The initial values are (0.5,0.3). (c)-(d) For 𝜏=0.05<𝜏₀, the positive equilibrium 𝐸^∗ is stable with an unstable periodic orbit. The initial values are (0.4,0.258) and (0.5,0.3). (e)-(f) For 𝜏=0.65>𝜏₀, the positive equilibrium 𝐸^∗ is unstable with an stable periodic orbit. The initial values are (0.1578,0.18935) and (0.5,0.3).

(a)

(b)

(c)

(d)

(e)

(f)