An age-structured population model with delayed and space-limited recruitment

A new age-structured model for a closed population with space-limited recruitment is proposed. The problem incorporates a time delay in the settlement process representing, for a marine population of invertebrates, the pelagic larval phase previous to the sessile stage. The model possesses a nontrivial steady state which is investigated. For a deeper analysis of the stability of this equilibrium, depending on the delay, an appropriate numerical method is proposed. The nontrivial equilibrium of the numerical scheme, based on the representation of the solution along the characteristics lines, is also analyzed. For a test model associated with the dynamics of a population of barnacles, numerical experiments describing the asymptotic behavior of the solutions varying the delay are provided. In this case, the delay behaves as a destabilizing parameter of the dynamics of the model. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).