Stability of equations with a distributed delay, monotone production and nonlinear mortality (Q2857758)

The paper considers a class of models for the population dynamics in the case of monotone fecundity functions embedding distributed and unbounded delays and, nonlinear mortality functions. The main result of the paper states that under certain assumptions, the unique positive equilibrium is globally asymptotically stable and, in this case, all positive solutions of the system are permanent. The non-oscillatory behavior of the solutions is also demonstrated, if the initial function is non-oscillatory, either less or greater than the positive equilibrium. The results applied to different models from population dynamics show that the assumptions on the fecundity and mortality functions and on delays are less restrictive and also, necessary.