Abstract

This presentation is devoted to bifurcation problems for some classes of PDE arising in the context of population dynamics. The main difficulty in such a context is to understand the dynamical properties of a PDE with non-linear and non-local boundary conditions.

A typical class of examples is the so called age structured models. Age structured models have been well understood in terms of existence, uniqueness, and stability of equilibria since the 80’s. Nevertheless, up to recently, the bifurcation properties of the semiflow generated by such a system has been only poorly understood.

In this presentation, we will start with some results about existence and smoothness of the center mainfold, and we will present some general Hopf bifurcation results applying to age structured models. Then we will turn to normal theory in such a context. The point here is to obtain formula to compute the first order terms of the Taylor expansion of the reduced system.