Farkas JZ (2008) Structured populations: The stabilizing effect of the inflow of newborns from an external source and the net growth rate. Applied Mathematics and Computation, 199 (2), pp. 547-558. http://www.sciencedirect.com/science/journal/00963003; https://doi.org/10.1016/j.amc.2007.10.018
We investigate the effect of a positive population inflow of individuals from an external source on the dynamical behaviour of certain physisologically 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.
Structured population dynamics; population inflow; net reproduction ratio; stability; Population dynamics; Mathematical models
Applied Mathematics and Computation: Volume 199, Issue 2