Font Size: 

We consider a dissipative discrete-time model for the dynamics of two interacting populations in a prey-predator relationship. The induced reproductive response can cause both suppression and increase in prey reproduction. The system presents rich dynamics explored through bifurcation diagrams and analysis of the system’s fixed points. Our results can lead to the extinction of both species, the survival of preys, and the dynamic equilibrium between both populations. Furthermore, we identify in the parameter plane periodic structures similar to Arnold's tongues and shrimps, as well as periodic, quasi-periodic, chaotic, hyperchaotic, and multistability regions that endorse the three scenarios mentioned before.