The Complex Dynamics of a Stochastic Predator-Prey Model

Figure 1

The phase portraits of model (1.3). The parameters are taken as 𝑎=2,𝑏=0.25,𝑐=0.875,𝑒=1,𝑚=0.95,and𝑛=0.75,𝑓=0.8. In this case, 𝐸₀=(0,0) is a source, 𝐸₁=(4,0) and 𝐸₄=(0.31772,1.5846) are saddle points, and 𝐸₂=(0,071429) is a nodal sink, which is stable. The positive equilibrium 𝐸₃=(0.96454,2.3932) is locally asymptotically stable. The dashed curve is the 𝑥-nullcline 𝑓(𝑥,𝑦)=0, and the dotted curve is the 𝑦-nullcline 𝑔(𝑥,𝑦)=0.