J Austral Math Soc Ser B 31 pp434--453, 1990.

Functional differential equations determining steady size distributions for populations of cells growing exponentially

A. J. Hall and G. C. Wake

Abstract

A population of cells growing and dividing often goes through a phase of exponential growth of numbers, during which the size distribution remains steady. In this paper we study the function differential equation governing this steady size distribution in the particular case where the individual cells themselves are growing exponentially in size. A series solution is obtained for the case where the probability of cell division is proportional to any positive power of the cell size, and a method for finding closed-form solutions for a more general class of cell division functions is developed.

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Authors

A. J. Hall

Plant Physiology Division, DSIR, Palmerston North, New Zealand and Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand.

G. C. Wake

Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand.