Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

Figure 1

The bifurcation diagram of system (1) with 𝑎₁₁=0.1,𝑎₁₂=1,𝑎₂₁=3/2, and 𝑚=2, where 𝐿1∶𝑟₁=−(2/9)𝑟²₂+𝑟₂/3,𝐿2∶𝑟₁=(8/9)𝑟²₂((3/2)−𝑟₂)/(2𝑟₂)−(4/3)𝑟₂((3/2)−𝑟₂), and 𝐿3∶𝑟₁=((16/9)𝑟₂+(1/6))((3/2)−𝑟₂)/(2𝑟₂).