Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays

Figure 1

Graphs of the equations in (12). 𝐿₃ is the boundary condition (𝑎₃=𝑎₃₂𝑣₂/(𝑚₂+𝑣₂)) and 𝐿₂ corresponds to −𝑎₂+𝑎₂₁(𝑣₁/(𝑚₁+𝑣₁))−𝑎₂₂𝑣₂=0, while 𝐿₁ corresponds to 𝑎₁−𝑎₁₁𝑣₁−𝑎₁₂𝑣₂/(𝑚₁+𝑣₁)=0. Intersection point between 𝐿₁ and 𝐿₂ gives the positive solution (𝑣^∗₁,𝑣^∗₂) to (12). Parameter values are listed in the example in Section 4.