Bifurcations of equilibria of a non-linear age structured model

Abstract

M. E. Gurtin and R. C. MacCamy investigated a non-linear age-structured population dynamical model, which served as one of the basic non-linear population dynamical models in the last three decades. They described a characteristic equation but they did not use it to discuss stability of equilibria of the system in certain special cases. In a recent paper, M. Farkas deduced a characteristic equation in another form. This characteristic equation enabled us to prove results about the stability of stationary age distributions of the system. In the present paper we are going to investigate how equilibria arise and change their stability as a basic parameter of the system varies.