Hopf bifurcation and the stability of non-linear age-dependent population models

Abstract

The possibility of Hopf bifurcation into stable orbits is considered for the Gurtin-MacCamy model of age-dependent population dynamics, in which the mortality function depends only on the population while fertility is a fairly general function of age as well as population. In addition an algorithm is produced which provides a necessary condition for Hopf bifurcation to occur for arbitrary systems of ordinary differential equations.