Persistence in seasonally varying predator-prey systems with Allee effect

Abstract

A generalized seasonally-varying predator-prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the trophic interaction functions. General conditions for coexistence are determined, both in the case of weak and strong Allee effect. Finally, a modified Leslie-Gower predator-prey model with Allee effect is investigated. Numerical results illustrate the qualitative behaviors of the system, in particular the presence of periodic orbits.