Bifurcation analysis of a ratio-dependent prey-predator model with the Allee effect

► We considered a predator-prey system with an Allee effect and the ratio-dependent predation. ► We have completed a full parametric analysis of the model. ► We compared the dynamics of the system for the cases of strong and weak Allee effects as well as the same system with the logistic growth rate. ► We revisit the paradox of enrichment and the paradox of biological control.