Figure 2.

Control of proliferation by random fluctuations. The typical time courses of the populations described by Eq. (2) are shown for growth rates given by all the combinations of Eqs (21), (22) and (23) with Eqs (15), (16) and (17) and for fluctuating parameter $c=\overline{c}+\epsilon (t)$. The thin lines correspond to different realizations of the random fluctuations, which are the same for all panels. The external fluctuations ε(t) follow a dichotomous random process with zero mean, standard deviation σ = 0.5, and correlation time τ = 0.05. The values of the remaining parameters are γ = 1, r₀ = 1, $\overline{c}=1$, and c₀ = 1. The initial condition is N = 0.5. The continuous thick line corresponds to the average behavior $e^{\overline{y}}$ given by Eq. (3) and the dashed thick lines correspond to $e^{\overline{y}+\sqrt{\langle {\eta }^2\rangle }}$ and $e^{\overline{y}-\sqrt{\langle {\eta }^2\rangle }}$ from Eqs (3) and (5).