Complex bifurcation phenomena seized in a discrete ratio-dependent Holling-Tanner predator-prey system

Using the semi-discretization method, one revisits a predator-prey model with a ratio-dependent Holling-Tanner functional response, which was previously explored using the forward Euler method. Some complex bifurcation phenomena are found in a new discrete system. In particular, one observes some dynamical differences between the two discrete methods not only in the type of fixed point but also in the existence of bifurcation. Numerical simulations are presented to illustrate the derived results.