Global behavior for an age-dependent population model with logistic term and periodic vital rates

Abstract

We investigate the large-time behavior of a nonlinear age-dependent population model with logistic term and T-periodic vital rates. We prove that there exists at most two T-periodic and nonnegative solutions of the given model, one of them being the trivial one. We show that for any initial distribution of population the solution tends to zero or to the nontrivial nonnegative T-periodic solution, if such solution exists. A numerical algorithm to approximate the solution corresponding to a given initial datum as well as the nontrivial nonnegative T-periodic solution of the given model is constructed. Results of the numerical tests are given.