Stability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect

Abstract

The Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population. In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed. Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.