Affiliations: Institute of Mathematics, Polish Academy of Sciences and Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland. [email protected] | Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland. [email protected]
Note: [] Address for correspondence: Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland
Abstract: We study a non-linear age-structured discrete-time population model and give necessary and sufficient conditions for stability of a positive stationary point. In the case of semelparous species we show that the population converges locally to a population consisted only of individuals at one age. It means that the long-time behaviour of the population depends only on an one-dimensional transformation g. If the reproduction age is an even number we prove that the positive stationary point is unstable and numerical simulations suggest that in this case almost all trajectories behave asymptotically as trajectories corresponding to g.
