Structured populations: The stabilizing effect of the inflow of newborns from an external source and the net growth rate

We investigate the effect of a positive population inflow of individuals from an external source on the dynamical behaviour of certain physiologically structured population models. We treat a size-structured model with constant inflow and nonlinear birth rate and an age-structured model with nonlinear (density dependent) inflow and linear birth rate. Analogously to the inherent net reproduction rate we introduce a net growth rate and discuss how this net growth rate can be related to our stability/instability conditions.