title: On the characteristic equation λ = α1 + (α2 + α3λ)e(-λ) and its use in the context of a cell population model.
abstract: In this paper we characterize the stability boundary in the (α1, α2)-plane, for fixed α3 with −1 < α3 < +1, for the characteristic equation from the title. Subsequently we describe a nonlinear cell population model involving quiescence and show that this characteristic equation governs the (in)stability of the nontrivial steady state. By relating the parameters of the cell model to the αi we are able to derive some biological conclusions.
authors.affiliation: Mathematical Institute, University of Utrecht, Utrecht, The Netherlands.
authors.forename: Odo
authors.initials: O
authors.lastname: Diekmann
authors.affiliation: TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062, Dresden, Germany.
authors.forename: Philipp
authors.initials: P
authors.lastname: Getto
authors.affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan. nakata@ms.u-tokyo.ac.jp.
authors.forename: Yukihiko
authors.initials: Y
authors.lastname: Nakata
mesh_terms: D059447:Cell Cycle Checkpoints; D048708:Cell Growth Processes; D049109:Cell Proliferation; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics
keywords: 34K20; 37N25; 45D05; 65L03; 92D25