  We study a discrete host-parasitoid system where the host population follows
the classical Ricker functional form and is also subject to Allee effects. We
determine basins of attraction of the local attractors of the single population
model when the host intrinsic growth rate is not large. In this situation,
existence and local stability of the interior steady states for the
host-parasitoid interaction are completely analyzed. If the host's intrinsic
growth rate is large, then the interaction may support multiple interior steady
states. Linear stability of these steady states is provided.
