Effects of prey over-undercrowding in predator-prey systems with prey-dependent trophic functions

The local dynamics of a two-trophic chain in the presence of both overcrowding and undercrowding effects on prey growth is investigated. The starting point is given by a general predator-prey system, in which the prey growth rate and the trophic interaction function are defined only by some properties determining their shapes; in particular, the prey growth function is assumed to model a strong Allee effect. A stability analysis of the system using the predation efficiency as bifurcation parameter is performed; conditions for the existence and stability of extinction and coexistence equilibrium states are determined, and peculiar features of the dynamics exhibited by the system are presented, with particular attention to limit cycles and bistability situations. Results are compared with those obtained when overcrowding and undercrowding effects are considered separately.