Original Research ArticleForaging facilitation among predators and its impact on the stability of predator-prey dynamics

- Rosenzweig-MacArthur-like model with predator foraging facilitation is studied.
- New stabilizing and destabilizing mechanisms are provoked by foraging facilitation.
- Hopf, Bogdanov-Takens, homoclinic and transcritical bifurcations are found.
- An inner Allee effect for the predators is shown.
- The impact to the risk of extinction is discussed.
- Stable are moderate density populations for higher level of predator facilitation.

Predator foraging facilitation may strongly influence the dynamics of a predator-prey system. This behavioral pattern is well-observed in real life interactions, but less is known about its possible impacts on the predator-prey dynamics. In this paper we analyze a modified Rosenzweig-MacArthur model, where a predator-dependent family of functions describing predator foraging facilitation is introduced into the Holling type II functional response. As the general assumption of foraging facilitation is that higher predator densities give rise to an increased foraging efficiency, we model predator facilitation with an increasing encounter rate function. Using the tools of bifurcation analysis we describe all the nonlinear phenomena that occur in the system provoked by foraging facilitation, these include the fold, Hopf, transcritial, homoclinic and Bogdanov-Takens bifurcation. We show that foraging facilitation can stabilize the coexistence in the predator-prey system for specific rates, but in most of the cases it can have fatal consequences for the predators themselves.