Comment on “Correlated noise in a logistic growth model”

We argue that the results published by Ai et al. [Phys. Rev. E 67, 022903 (2003)] on “correlated noise in logistic growth” are not correct. Their conclusion that, for larger values of the correlation parameter $\lambda$, the cell population is peaked at $x=0$, which denotes a high extinction rate, is also incorrect. We find the reverse behavior to their results, that increasing $\lambda$ promotes the stable growth of tumor cells. In particular, their results for the steady-state probability, as a function of cell number, at different correlation strengths, presented in Figs. 1 and 2 of their paper show different behavior than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation that at small values of cell number the steady-state probability increases as the correlation parameter is increased is also questionable. Another striking feature in their Figs. 1 and 3 is that, for the same values of the parameters $\lambda$ and $\alpha$, their simulation produces two different curves, both qualitatively and quantitatively.

Figure 1

Plot of $p_{st}\left(x\right)$ as a function of $x$ for low values of correlation parameter $\lambda$. $D=0.3$, $\alpha =3.0$, $a=1.0$, $b=0.1$, and $\lambda =0.0,0.2,0.3,0.5$. All the parameter values are in arbitrary units.

Figure 2

Plot of $p_{st}\left(x\right)$ as a function of $x$ for low values of correlation parameter $\lambda$. $D=0.3$, $\alpha =3.0$, $a=1.0$, $b=0.1$, and $\lambda =0.6,0.7,0.9,0.99$. All the parameter values are in arbitrary units.