On the stability of steady size-distributions for a cell-growth process with dispersion

Abstract

The model discussed in this paper describes the evolution of the size-distribution of a population of cells in time. It is assumed that there is a degree of stochasticity in the growth process of each individual cell in the population. This manifests itself as a dispersion term in the differential equation for the evolution of the size-distribution of the overall population. We study the stability of the Steady Size-Distributions (SSDs) of the model (the spatial components of separable solutions) and show that given a set of parameters where an SSD exists, it is unique and globally asymptotically stable.