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

Odo 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

Odo Diekmann^*, H. J.A.M. Heijmans, H. R. Thieme

^*Corresponding author for this work

Sub Mathematical Modeling

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

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
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
Publication status	Published - 1986

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title = "On the stability of the cell-size distribution II: Time-periodic developmental rates",

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.",

author = "Odo Diekmann and Heijmans, {H. J.A.M.} and Thieme, {H. R.}",

year = "1986",

doi = "10.1016/0898-1221(86)90176-8",

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T2 - Time-periodic developmental rates

AU - Diekmann, Odo

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

AU - Thieme, H. R.

PY - 1986

Y1 - 1986

N2 - 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.

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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DO - 10.1016/0898-1221(86)90176-8

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 4-5, part A

ER -

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

Abstract

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