Coexistence of a one-prey two-predators model with ratio-dependent functional responses

We examine the positive coexistence of one prey and two competing predators in an interacting system with ratio-dependent functional responses under a hostile environment. Furthermore, we examine the extinction conditions for all three interacting species and for one or two of the three species. In addition, we present the biological interpretation and simulations based on the result. The methods employed are a comparison argument for the elliptic problem and the fixed-point theory applied to a positive cone on a Banach space.