Asymptotic Similarity and Malthusian Growth in Autonomous and Nonautonomous Populations

We consider the dynamics of a multistate age-structured population as a nonautonomous system of partial differential equations. This system generates a positive process on a space of bounded functions. We give sufficient conditions for asymptotic similarity of this process, i.e., we show when the asymptotic behaviour of the process at t → ∞ is independent of the initial distribution.