Mathematical analysis of a population model with an age-weight structured two-stage life history: asymptotic behavior of solutions
The paper deals with a model for the dynamics of a physiologically structured population of individuals whose life cycle is divided in two stages with a different structure variable for each stage. The first stage is structured by the weight, while the second one is structured by the age, and the exit from the first stage occurs when a threshold weight is attained. This model is based on the classical Lotka-MacKendrick linear model, which integrating along the characteristic lines can be reduced to the so-called delayed renewal equation including a constant delay. This delay can be viewed as the time spent by individuals in the first stage to reach the weight threshold. By using the Laplace transform, the authors investigate the asymptotic behavior of solutions for the model above, and then they discuss the growth rate and the maturation threshold on the long-term behavior of solutions.
scientific article; zbMATH DE number 6345566