Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation

Figure 2

Two of the species will die out in probability. The red lines represent the solution of system (1), while the blue lines represent the solution of system (3) with (𝑥₁(0),𝑥₂(0),𝑥₃(0))=(1,0.8,0.5), 𝑎₁=0.4, 𝑎₂=0.4, 𝑎₃=0.1, 𝑏₁₁=0.1, 𝑏₁₂=0.1, 𝑏₂₁=0.6, 𝑏₂₂=0.6, 𝑏₂₃=0.6, 𝑏₃₂=0.8, and 𝑏₃₃=0.6. The red lines represent the solution of system (1), while the blue lines represent the solution of system (3) with 𝜎₁=0.02, 𝜎₂=3, and 𝜎₃=0.01.