Stability of an Age-Dependent Population

This paper considers a nonlinear deterministic population model in which the death rate rises as the population grows. It is an age-dependent version of a logistic population whose growth is controlled by limited resources and is in the form of a partial differential equation with respect to time and age. We prove that the solution of our equation behaves asymptotically just like the solution of the logistic equation ${{dN} / {dt}} = N(a - bN)$ and is, therefore, globally asymptotically stable. This implies that there are no steady oscillations, and that in the long run the population size and age-structure become fixed, independent of the initial conditions. Possible applications in fish and animal population dynamics are studied.