Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation

Figure 1

Solution of system (3) with initial conditions 𝑥₁(0)=𝑥₂(0)=𝑥₃(0)=0.2 and 𝑟=0.6, 𝑑₁=0.2, 𝑎₁₁=0.3, 𝑏=0.8, 𝑎₁₃=0.6, 𝑑₂=0.3, 𝑎₂₂=0.2, 𝑎₂₃=0.3, 𝑑₃=0.1, 𝑘₁=5/6, 𝑘₂=0.8, 𝑎₃₃=0.2, Δ𝑡=0.01, 𝑚=0.3, 𝑛=0.1, 𝛼=2, and 𝛽=1. (a) 𝜎₁=𝜎₂=𝜎₃=0. (b) 𝜎²₁=1.9, 𝜎²₂=0.6, and 𝜎²₃=1.9. (c) 𝜎²₁=20, 𝜎²₂=20, and 𝜎²₃=20.

(a)

(b)

(c)