Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters

Figure 2

The time histories and phase portrait of system (4.1) with the following parameters: 𝑎=0.5,𝑏=0.5,𝑐=2,𝜛=2,𝑑=0.2, and 𝜏=1.8>𝜏₀≈1.7355. Hopf bifurcation occurs from the positive equilibrium 𝐸_∗(𝑥^∗,𝑦^∗)=(0.5014,1.3108). The initial value is (0.2, 2).

(a)

(b)

(c)

(d)