Stability analysis of a stochastic model for biomolecular selection
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.
scientific article; zbMATH DE number 3910199