If the modified stability parameter is sufficiently large, but smaller than a critical value $\delta\Delta_{max}^{'crit}$, or $\tau_{zf}/\tau_\eta<\zeta_{crit}$, an oscillating island appears (region $2$ in Fig.\[fig8\](a)). Its maximum width remains below $w_{seed}$ and is roughly proportional to $\tau_{zf}$. Finally, when the critical values are exceeded, the full NTM is triggered and the system settles in a state with $w$ oscillating around $w_{sat}$ (region $3$ in Fig.\[fig8\](a)). The approximate boundaries of these regimes \[obtained solving Eq.\[13\] numerically\] are sketched in Fig.\[fig8\](a), for a case with $\Delta'=-1$, $C_0=0.25$, $w_{boot}=w_{pol}=0.025$, which correspond to reasonable experimental values [@LeHaye2006; @Buttery2002]. For clarity, in Fig.\[fig8\] (b) we show the time evolution of two cases with $\delta\Delta'_{max}=2.94$, one just below $\zeta_{crit}$ ( $\zeta=0.05$ for the solid line) and one above ($\zeta=0.1$ for the dashed line). For the same two solutions, we plot in Fig.\[fig8\] (c) the phase diagram, which describes how $dw/dt$ and $w$ are related during the evolution of the perturbation. Two dots in Fig.\[fig8\](a) display the position of these cases in the $\delta\Delta'_{max}-\zeta$ space.

Obviously, in a realistic situation the time evolution of $\delta\Delta'$ would be erratic and Eq.\[13\] would become a stochastic differential equation. We expect that this would make the triggering mechanism easier, with 