Bifucations and Hydra effects in Rosenzweig-MacArthur model

In this paper, a Rosenzweig-MacArthur predator-prey model with intraspecific competition of predators and Holling type II functional response with a prey refuge is investigated by using dynamical approach. We study the number of positive equilibria, the local and global dynamics including Hopf bifurcation, saddle-node bifurcation, Bautin bifurcation. We provide the coexistence of stable and unstable limit cycles. In particular, we show the hydra effect that describes the positive effect of the predator’s mortality, as well as the positive effects of prey refuge and intraspecific competition among predators, on the predator’s population density. Furthermore, numerical simulations demonstrate the theoretical results including the hydra effect region and trophic cascade.