  Star formation histories (SFH) of early (6$<z<$12) galaxies have been found
to be highly stochastic in both simulations and observations, while at
$z\lesssim$6 the presence of a main sequence (MS) of star-forming galaxies
imply secular processes at play. In this work, we aim at characterising the SFH
variability of early galaxies as a function of their stellar mass and redshift.
We use the JADES public catalogue and derive the physical properties of the
galaxies as well as their SFH using the spectral energy distribution modelling
code CIGALE. To this aim, we implement a non-parametric SFH with a flat prior
allowing for as much stochasticity as possible. We use the SFR gradient, an
indicator of the movement of galaxies on the SFR-$M_\ast$ plane, linked to the
recent SFH of galaxies. This dynamical approach of the relation between the SFR
and stellar mass allows us to show that, at $z>9$, 87% of massive galaxies,
($\log(M_\ast/M_\odot)\gtrsim$9), have SFR gradients consistent with a
stochastic star-formation activity during the last 100 Myr, while this fraction
drops to 15% at $z<7$. On the other hand, we see an increasing fraction of
galaxies with a star-formation activity following a common stream on the
SFR-$M_\ast$ plane with cosmic time, indicating that a secular mode of
star-formation is emerging. We place our results in the context of the observed
excess of UV emission as probed by the UV luminosity function at $z\gtrsim10$,
by estimating $\sigma_{UV}$, the dispersion of the UV absolute magnitude
distribution, to be of the order of 1.2mag and compare it with predictions from
the literature. In conclusion, we find a transition of star-formation mode
happening around $z\sim9$: Galaxies with stochastic SFHs dominates at
$z\gtrsim9$, although this level of stochasticity is too low to reach those
invoked by recent models to reproduce the observed UV luminosity function.
