Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay

Figure 1

When 𝜏=1.11<𝜏₀, the positive equilibrium 𝐸⁺=(2.8333,0.8333,1.8056) is asymptotically stable. (a) shows the trajectories graphs of the system (4.1) with initial data 𝑋(𝑡)=2,𝑆₁(𝑡)=2,𝐼₂(𝑡)=2. (b) shows the phase portrait of system (4.1).

(a)

(b)