Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation

Figure 1

The solution of system (1) and system (3) with (𝑥(0),𝑦(0))=(2,1), 𝑟=1.2, 𝜇=0.3,𝐾=4, 𝑐=0.2,𝑚𝑐=0.1. The red lines represent the solution of system (1), while the blue lines represent the solution of system (3) with 𝜎₁=0.01, 𝜎₂=0.01 in (a) and 𝜎₁=0.06, 𝜎₂=0.08 in (b), respectively.

(a)

(b)