Dynamics of a Scalar Population Model with Delayed Allee Effect

Abstract

A scalar population model with delayed growth rate of Allee effect type is considered in this paper. The stability of equilibria and associated supercritical Hopf bifurcations are analyzed. The basins of attraction of the two locally stable equilibria are characterized in terms of parameter values. In particular, when the time delay is large, the basin of attraction of the persistence equilibrium and limit cycle shrinks to a single point, so a global extinction of population occurs as a combined result of Allee effect and time delay.