Asymptotic behaviour of a semilinear age-structured population model with a dynamics for the resource

A semilinear equation is considered for an age-structured population model with two groups, juveniles and adults, and with a dynamics for the resource. The death rates of young and adults are assumed to be decreasing functions of the amount of available resources. In a previous paper, the particular case of uniform increase of mortality was studied. Here, the general case with different death rates is undertaken using the semilinear formulation of the initial value problem. The existence, uniqueness, and the positivity of the solution is proved. Under biologically meaningful conditions, a description of the asymptotic behaviour of the population dynamics system is obtained, showing properties of stability, instability, and bifurcation of the equilibria and the existence of a compact global attractor which contains a coexistence equilibrium.