Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

Figure 1

(a) System (4) shows an unstable limit cycle when 𝑎=1.6, 𝛽=2, 𝑚=0.13095, and ℎ=0.128. 𝛿₂≈0.2220>𝛿=0.00249>𝛿≈0.00235; (b) System (4) shows a stable limit cycle when 𝑎=1.2, 𝛽=2, 𝑚=0.08235, and ℎ=0.08396. 𝛿₁≈0.0000391<𝛿=0.002919<𝛿≈0.003639.

(a)

(b)