Consequences of Allee Effects on Stability Analysis of the Population Model Xt+1=?xtf(xt?3)

Abstract

The stability conditions of equilibrium points of the population model Xt+1 = lambda X(t)f(Xt-3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.