A discrete-time Holling-Tanner model with ratio-dependent functional response is
examined. We show that the system experiences a flip bifurcation and Neimark-Sacker
bifurcation or both together at positive fixed point in the interior of R2
+ when one of
the model parameter crosses its threshold value. We concentrate our attention to
determine the existence conditions and direction of bifurcations via center manifold
theory. To validate analytical results, numerical simulations are employed which
include bifurcations, phase portraits, stable orbits, invariant closed circle, and attracting
chaotic sets. In addition, the existence of chaos in the system is justified numerically by
the sign of maximum Lyapunov exponents and fractal dimension. Finally, we control
chaotic trajectories exists in the system by feedback control strategy.