A Predator-Prey Model in the Chemostat with Time Delay

Figure 3

The two-parameter bifurcation diagram of 𝐸₊ in 𝜏 and 𝛼 parameter space. Parameters are the same as in Figure 1 (i.e., 𝐷=Δ=1,𝑘=24) except now both 𝜏 and 𝛼 are allowed to vary. For any pair (𝛼,𝜏) on the closed curve, there is a Hopf bifurcation of 𝐸₊. Inside the closed curve, there is a periodic solution surrounding 𝐸₊. For any (𝛼,𝜏) outside the closed curve and below 𝜏=𝜏_𝑐, the coexistence equilibrium 𝐸₊ is stable.