Dynamics of a discrete-time predator-prey system with ratio-dependent functional response

The aim of this article is to analyze the qualitative behavior of a discrete-time predator-prey system with ratio-dependent functional response. We express algebraically the conditions for the existence of a positive fixed point, and determining its stability. We also prove that the system has a Neimark-Sacker bifurcation when some parametric conditions are satisfied. The Chaos control is nicely studied by applying the hybrid control method. Finally, we present some numerical simulations in order to verify the theoretical results we have shown.