Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation

Figure 3

One of the species or both 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=−0.1, 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.