Stabilizing Effect of Prey Refuge and Predator’s Interference on the Dynamics of Prey with Delayed Growth and Generalist Predator with Delayed Gestation

Figure 5

Bifurcation diagram of the system (3) with respect to 𝜏₁ in Case 5. (a) is drawn in the three-dimensional space (𝜏₁,𝑥,𝑦). (b) and (c) are the time evolutions for 𝜏₁=0.48<𝜏₁₀=0.5296 (system is stable) and 𝜏₁=0.54>𝜏₁₀=0.5296 (system is unstable), respectively. A Hopf bifurcation exists at 𝜏₁=0.5296. Here, 𝜏₂=0.4∈[0,0.4205).

(a) 𝜏₂=0.4

(b) 𝜏₁=0.48

(c) 𝜏₁=0.54