On the stability of the cell size distribution

O. Diekmann, H. J A M Heijmans, Horst Thieme

Research output: Contribution to journalArticle

135 Citations (Scopus)

Abstract

A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.

Original languageEnglish (US)
Pages (from-to)227-248
Number of pages22
JournalJournal of Mathematical Biology
Volume19
Issue number2
DOIs
StatePublished - Apr 1984
Externally publishedYes

Fingerprint

Cell Size
growth models
Balance Laws
Semigroup Theory
Structured Populations
Stable Distribution
Cell Population
First order differential equation
Growth
Partial differential equations
Compactness
Partial differential equation
Cells
cells
Term
Model
Population
Form

Keywords

  • Balance equation
  • First-order partial differential equation
  • Reproduction by fission
  • Size-dependent population growth
  • Stable size distribution
  • Transformed arguments

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

Cite this

On the stability of the cell size distribution. / Diekmann, O.; Heijmans, H. J A M; Thieme, Horst.

In: Journal of Mathematical Biology, Vol. 19, No. 2, 04.1984, p. 227-248.

Research output: Contribution to journalArticle

Diekmann, O. ; Heijmans, H. J A M ; Thieme, Horst. / On the stability of the cell size distribution. In: Journal of Mathematical Biology. 1984 ; Vol. 19, No. 2. pp. 227-248.
@article{e96fd50749f649c89409bae2cfa3478c,
title = "On the stability of the cell size distribution",
abstract = "A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.",
keywords = "Balance equation, First-order partial differential equation, Reproduction by fission, Size-dependent population growth, Stable size distribution, Transformed arguments",
author = "O. Diekmann and Heijmans, {H. J A M} and Horst Thieme",
year = "1984",
month = "4",
doi = "10.1007/BF00277748",
language = "English (US)",
volume = "19",
pages = "227--248",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "2",

}

TY - JOUR

T1 - On the stability of the cell size distribution

AU - Diekmann, O.

AU - Heijmans, H. J A M

AU - Thieme, Horst

PY - 1984/4

Y1 - 1984/4

N2 - A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.

AB - A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.

KW - Balance equation

KW - First-order partial differential equation

KW - Reproduction by fission

KW - Size-dependent population growth

KW - Stable size distribution

KW - Transformed arguments

UR - http://www.scopus.com/inward/record.url?scp=0021153388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021153388&partnerID=8YFLogxK

U2 - 10.1007/BF00277748

DO - 10.1007/BF00277748

M3 - Article

AN - SCOPUS:0021153388

VL - 19

SP - 227

EP - 248

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -