Weak Allee effect in a predator-prey system involving distributed delays

in this paper we study the influence of weak allee effect in a predator-prey system model. this effect is included in the prey equation and we determine conditions for the occurrence of hopf bifurcation. the stability properties of the system and the biological issues of the memory and allee models on the coexistence of the two species are studied. finally we present some simulations which allow one to verify the analytical conclusions obtained. mathematical subject classification: primary: 34c25; secondary: 92b05.