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

Figure 3

Bifurcation diagram of the system (3) with respect to 𝜏₂ in Case 3. (a) is drawn in the three-dimensional space (𝜏₂,𝑥,𝑦). (b) and (c) are the time evolutions for 𝜏₂=0.4<𝜏₂₀=0.4444 (system is stable) and 𝜏₂=0.48>𝜏₂₀=0.4444 (system is unstable), respectively. A Hopf bifurcation exists at 𝜏₂=0.4444. Here, 𝜏₁=0.45∈[0,0.5329).

(a) 𝜏₁=0.45

(b) 𝜏₂=0.4

(c) 𝜏₂=0.48