Literature DB >> 3199044

Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle.

J Tyrcha1.   

Abstract

A new mathematical model of the cell cycle is presented which generalizes the probabilistic/deterministic model of Lasota-Mackey and the tandem model of Tyson and Hannsgen. By the use of a multiplicative (exponential) Lyapunov function a stability theorem is proved, parallel to the results of Lasota-Mackey. Some open problems related to the tandem model are also solved.

Mesh：

Year:  1988        PMID： 3199044     DOI： 10.1007/bf00276374

Source DB:  PubMed          Journal:  J Math Biol        ISSN： 0303-6812            Impact factor:   2.259


  5 in total

Review 1.  Mathematics of microbial populations.

Authors:  P R Painter; A G Marr
Journal:  Annu Rev Microbiol       Date:  1968       Impact factor: 15.500

2.  Cell growth and division: a deterministic/probabilistic model of the cell cycle.

Authors:  J J Tyson; K B Hannsgen
Journal:  J Math Biol       Date:  1986       Impact factor: 2.259

3.  Globally asymptotic properties of proliferating cell populations.

Authors:  A Lasota; M C Mackey
Journal:  J Math Biol       Date:  1984       Impact factor: 2.259

4.  The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions.

Authors:  J J Tyson; K B Hannsgen
Journal:  J Theor Biol       Date:  1985-03-07       Impact factor: 2.691

5.  Sloppy size control of the cell division cycle.

Authors:  J J Tyson; O Diekmann
Journal:  J Theor Biol       Date:  1986-02-21       Impact factor: 2.691
  5 in total

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