Analysis of Stochastic Delay Predator-Prey System with Impulsive Toxicant Input in Polluted Environments

Figure 1

Solutions of system (3) for 𝑟₁₀=0.85, 𝑟₂₀=0.05, 𝑟₁₁=𝑟₂₁=1, 𝑎₁₁=0.4, 𝑎₁₂=0.4, 𝑎₂₁=0.3, 𝑎₂₂=0.3, 𝜏₁=3, 𝜏₂=8, 𝛼²₂=0.1, 𝑘_𝑖=𝑔_𝑖=𝑚_𝑖=0.1, 𝑖=1,2, ℎ=0.5, 𝑏=0.6, 𝛾=12, 𝑥₁(0)=0.9, 𝑥₂(0)=0.5, 𝐶₀(0)=𝐶_𝑒(0)=0.1, and step size Δ𝑡=0.001. (a) is with 𝛼²₁/2=0.82; (b) is with 𝛼²₁/2=0.65; (c) is with 𝛼²₁/2=0.2.

(a)

(b)

(c)