Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$

Abstract

The stability conditions of equilibrium points of the popul ation model $X_{t+1}=lambda X_tf(X_{t-3})$ with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population de nsity. Analysis and numerical simulations show that Allee effects h ave both stabilizing and destabilizing effects on population dynamics with delay.