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

Figure 4

(a) System (4) shows a cusp of codimension 2 when 𝑎=1.6, 𝛽=2, 𝑚=(1/4)(1−𝛽/(𝑎𝛽+1)), ℎ=(1/4)(𝛽/(𝑎𝛽+1)−1)²+𝑚𝛽/(𝑎𝛽+1), 𝛿=1/(𝑎𝛽+1)², and 𝜇₁=0, 𝜇₂=0; (b) the cusp of codimension 2 break into an unstable focus 𝐸₁ and a hyperbolic saddle 𝐸₂ when 𝜇₁=−0.0132, 𝜇₂=−0.02.

(a)

(b)