On the stability of the cell-size distribution II: Time-periodic developmental rates

O. Diekmann; H. J.A.M. Heijmans; H. R. Thieme

doi:10.1016/0898-1221(86)90176-8

On the stability of the cell-size distribution II: Time-periodic developmental rates

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

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

A deterministic model for the growth of a size-structured proliferating cell population is analyzed. The developmental rates are allowed to vary with time. For periodically varying rates stability of the cell-size distribution is shown under similar conditions for the growth rate of individual cells as found before in the time-homogeneous case. Strongly positive quasicompact linear operators on Banach lattices serve as powerful abstract tools. Finally, the autonomous case is revisited and the conditions for stability found in [1] are relaxed.

Original language	English (US)
Pages (from-to)	491-512
Number of pages	22
Journal	Computers and Mathematics with Applications
Volume	12
Issue number	4-5 PART A
DOIs	https://doi.org/10.1016/0898-1221(86)90176-8
State	Published - 1986
Externally published	Yes

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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abstract = "A deterministic model for the growth of a size-structured proliferating cell population is analyzed. The developmental rates are allowed to vary with time. For periodically varying rates stability of the cell-size distribution is shown under similar conditions for the growth rate of individual cells as found before in the time-homogeneous case. Strongly positive quasicompact linear operators on Banach lattices serve as powerful abstract tools. Finally, the autonomous case is revisited and the conditions for stability found in [1] are relaxed.",

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AU - Diekmann, O.

AU - Heijmans, H. J.A.M.

AU - Thieme, H. R.

PY - 1986

Y1 - 1986

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AB - A deterministic model for the growth of a size-structured proliferating cell population is analyzed. The developmental rates are allowed to vary with time. For periodically varying rates stability of the cell-size distribution is shown under similar conditions for the growth rate of individual cells as found before in the time-homogeneous case. Strongly positive quasicompact linear operators on Banach lattices serve as powerful abstract tools. Finally, the autonomous case is revisited and the conditions for stability found in [1] are relaxed.

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JO - Computers and Mathematics with Applications

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IS - 4-5 PART A

ER -

On the stability of the cell-size distribution II: Time-periodic developmental rates

Abstract

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