Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge

Figure 3

Under the condition of 𝜏₁=1.28, (a) 𝐸_∗ is asymptotically stable equilibrium at 𝜏₂=1.32; (b) 𝐸_∗ loses stability and the Hopf bifurcation occurs at 𝜏₂=5.83; (c) a chaotic solution occurs at 𝜏₂=7.9; (d) the largest Lyapunov exponent diagram of system (55) for variable 𝜏₂.

(a)

(b)

(c)

(d)