Abstract: We present Delay Equations describing age-structured cell population dynamics where the cell population is divided into proliferative and quiescent cells. We derived a characteristic equation for an interior equilibrium and analyzed the model in the framework of [1,2]. We will show how to use the characteristic equation to determine stability boundaries for the interior equilibrium in a two-parameter plane. This is a joint work with Tomas Alarcon, Odo Diekmann and Philipp Getto.

[1] O. Diekmann, S.A. van Gils, S.M.V. Lunel, H.O. Walther (1995) Delay equations: functional, complex,and nonlinear analysis, vol 110 of Applied Mathematical Sciences. Springer-Verlag

[2] O. Diekmann, Ph. Getto, M. Gyllenberg (2007) Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars. SIAM J Math Anal 39:1023-1069