The asymptotic behavior of a single population model with space-limited and stage-structure

In this paper, a single population model with space-limited and stage-structure is considered. Sufficient conditions for uniform persistence of the model are obtained by the theory of infinite dimensional dynamical systems. Then by applying the theory of Hopf bifurcation and the Browder fixed point theorem, sufficient conditions for the limit cycle of the model existing in small range and large range are, respectively, obtained.