Large time behavior in a density-dependent population dynamics problem with age structure and child care
Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the environmental influence depending on the total density of the juvenile and adult individuals. An existence and uniqueness theorem is proved, a class of separable solutions is constructed, and the large time behavior of the general and separable solutions is given for the non-dispersing population with stationary vital rates. The steady-state and separable solutions are constructed and the large time behavior of the separable solutions is studied for the population with the spatial dispersal.