The influence of past in a population system involving intraspecific competition and Allee effect

This paper investigates a predator-prey model incorporating Allee effect and intraspecific competition with fading memory. In fact, the rate of past influence may have an essential role on the dynamics of both species since the density of predator depends not only on the prey quantity at present, but also on the prey quantity at recent past. The existence conditions for the steady states and their stability are presented. A single parameter numerical continuation with respect to Allee effect threshold, intraspecific competition and predator death ratio is performed for a low and high rate of past influence. Change in the memory term leads to a change in the direction of the Hopf bifurcation. The mathematical formulations are complemented with numerical simulations.