Stability in a Nonlinear Population Maturation Model

We consider models for population structured by maturation/maturation speed proposed by Rotenberg. It is a variant of transport equations for age-structured populations which presents particularly interesting mathematical difficulties. It allows one to introduce more stochasticity in the birth process and in the aging phenomena. We present a new method for studying the time asymptotics which is also illustrated on the simpler McKendrick–Von Foerster model. The nonlinear variants of these models are shown to exhibit either nonlinear stability or periodic solutions depending on the datum.