Coexistence in seasonally varying predator–prey systems with Allee effect. (October 2020) - Rebelo, C.; Soresina, C.
Abstract: A general 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 functional responses. 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. Highlights: A general predator–prey model with seasonality and Allee effect on the prey growth. Theoretical results are obtained for a general class of models. Weak Allee effect: persistence of a periodic orbit via the basic reproduction number. Strong Allee effect: we used the degree theory to get periodic orbits. Numerical results illustrate the qualitative behaviors of the system.