A Predator-Prey Model in the Chemostat with Time Delay

Figure 2

Eigenvalues with the largest real parts of the characteristic equation (4.2) at 𝐸₊. Parameters are the same as in Figure 1 except 𝛼=1.3 for the TOP and 𝛼≈1.5 for the BOTTOM graph. Due to the scaling, the eigenvalues in the circle in the TOP graph seem indistinguishable from zero. In fact, they are a pair of complex eigenvalues with real parts slightly less than zero. As 𝛼 varies from 1.3 to 1.5, the pair of complex eigenvalues with largest real part becomes a pair of pure imaginary roots in the BOTTOM graph. The eigenvalue with the second largest real part remains equal to −1. This is consistent with our analytical results that showed that (4.2) has a constant eigenvalue −1 when 𝐷=Δ=1.