Stability analysis of a stochastic model for biomolecular selection
type: Item
instance of: scholarly article
title: Stability analysis of a stochastic model for biomolecular selection
zbMATH Open document ID: 0569.92015
DOI: 10.1007/BF02462015
published in: Bulletin of Mathematical Biology
publication date: 1984-01-01T00:00:00Z
review text: The paper analyses a model for biomolecular selection on the basis of a nonlinear birth and death process. It is assumed that the rates of replication and degradation per individual molecule are constants. In addition the author introduces a dilution factor that depends on the number of molecules of the particular species. The resulting master equation is analyzed by introducing the probability generating function. Since such a technique merely transfers the nonlinearity to the subsidiary equations that describe the characteristics, resort is made to an approximation scheme in which higher order cumulants (\(\geq 3)\) are neglected. Conclusions are drawn regarding the stability of the surviving species. Apparently the author appears to be unaware of the fact that the neglect of higher order cumulants may result in the probabilities failing to remain positive definite.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 3910199
zbMATH Keywords: linear stability approximation
zbMATH Keywords: biomolecular selection
zbMATH Keywords: nonlinear birth and death process
zbMATH Keywords: replication
zbMATH Keywords: degradation
zbMATH Keywords: dilution factor
zbMATH Keywords: master equation
zbMATH Keywords: probability generating function
zbMATH Keywords: stability of the surviving species
author: Hareton Leung
MaRDI profile type: Publication
Wikidata QID: Q52696977
cites work: Q3921169
cites work: Stochastic analysis of a nonlinear model for selection of biological macromolecules
full work available at URL: https://doi.org/10.1007/bf02462015
OpenAlex ID: W4253023627
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description: scientific article; zbMATH DE number 3910199