  In this paper, we investigate the global asymptotic stability of an
age-structured population dynamics model with a Ricker's type of birth
function. This model is a hyperbolic partial differential equation with a
nonlinear and nonlocal boundary condition. We prove a uniform persistence
result for the semi-flow generated by this model. We obtain the existence of
global attractors and we prove the global asymptotic stability of the positive
equilibrium by using a suitable Lyapunov functional. Furthermore, we prove that
our global asymptotic stability result is sharp, in the sense that Hopf
bifurcation may occur as close as we want from the region global stability in
the space of parameter.
