The Hopf Bifurcation for a Predator-Prey System with 𝜃-Logistic Growth and Prey Refuge

Figure 2

The infected steady state 𝐸^∗ of system (1) is asymptotically stable when 𝜃=4 (a), and unstable when 𝜃=5 (b). The rest parameter values are 𝑟=0.1, 𝐾=10, 𝛽=0.2, 𝑎=0.13, and 𝜀=0.3, and the initial values are 𝑥₀=8 and 𝑦₀=5.

(a)

(b)