Ratio-dependent predator-prey models of interacting populations

Ratio-dependent predator-prey models are increasingly favored by both the theoretical and experimental ecologists as a more suitable alternative to describe predator-prey interactions when the predators hunt seriously. In this article, the classical Bazykin's model is modified with ratio-dependent functional response. Stability and bifurcation situations of the system are observed. Since the ratio-dependent model always has difficult dynamics in the vicinity of the origin, the analytical behavior of the system near origin is studied completely. It is found that paradox of enrichment can happen to this system under certain parameter values, although the functional response is ratio-dependent. The parametric space for Turing spatial structure is determined. We also conclude that competition among the predator population might be beneficial for predator species under certain circumstances. Finally, ecological interpretations of our results are presented in the discussion section.