title: Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division.
abstract: A model of cell cycle kinetics is proposed, which includes unequal division of cells, and a nonlinear dependence of the fraction of cells re-entering proliferation on the total number of cells in the cycle. The model is described by a nonlinear functional-integral equation. It is analyzed using the operator semigroup theory combined with classical differential equations approach. A complete description of the asymptotic behavior of the model is provided for a relatively broad class of nonlinearities. The nonnegative solutions either tend to a stable steady state, or to zero. The simplicity of the model makes it an interesting step in the analysis of dynamics of nonlinear structure populations.
authors.affiliation: Department of Mathematics, University of Pau, France.
authors.forename: O
authors.initials: O
authors.lastname: Arino
authors.forename: M
authors.initials: M
authors.lastname: Kimmel
mesh_terms: D002453:Cell Cycle; D008954:Models, Biological