Stability for a competing system of hierarchical age-structured populations

In this paper,we are concerned with the stability for a model in the form of system of integro-partial differential equations,which governs the evolution of two competing age-structured populations.The age-specified environment is incorporated in the vital rates,which displays the hierarchy of ages.By a non-zero fixed-point result,we show the existence of positive equilibria.Some conditions for the stability of steady states are derived by means of semigroup method.Furthermore,numerical experiments are also presented.