Host-Parasitoid Systems with Predation-Driven Allee effects in Host

4 Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programs. In this article, we investigate the population dynamics of host-parasitoid systems with Allee effects induced by predation satiation in host to study the effects of Allee effects and parasitism as well as the timing of parasite’s attacking. The interactions of Allee effects and parasitism can lead to extremely complicated dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform 1) the local analysis to study the number of equilibria and their stability; and 2) the global analysis to study the extinction and permanence of host-parasitoid systems with Allee effects, for both parasitism attacking before and after the growth phase of host. The theoretical and numerical results suggest that i) Allee effects can generate and destroy interior equilibrium; ii) The timing of parasite’s attacking does not affect the boundary equilibria and their stability as well as the permanence condition; iii) The combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their hight population density. These results may have potential useful biological importance for biological conservation.