A short proof for Hopf bifurcation in Gurtin-MacCamy’s population dynamics model

In this paper, we provide a short proof for the Hopf bifurcation theorem in Gurtin-MacCamy’s population dynamics model. Here use Crandall and Rabinowitz’s approach, based on implicit function theorem. Compared with previous methods, here require age-specific birth rate to be slightly smoother (roughly of bounded variation), but have huge gain length proof.