  We present new experimental results on the quenching dynamics of an extended
thermo-convective system (a network array of approximately 100 convective
oscillators) going through a secondary subcritical bifurcation. We characterize
a dynamical phase transition through the nature of the domain walls (1D-fronts)
that connect the basic multicellular pattern with the new oscillating one. Two
different mechanisms of the relaxing dynamics at the threshold are
characterized depending on the crossing rate
$\mu=\frac{d\epsilon}{dt}|_{\epsilon=0}$ (where $\epsilon$ is the control
parameter) of the quenched transition. From the analysis of fronts, we show
that these mechanisms follow different correlation length scales $\xi \sim
\mu^{-\sigma}$. Below a critical value $\mu_c$ a slow response dynamics yields
a spatiotemporal coherent front with weak coupling between oscillators. Above
$\mu_c$, for rapid quenches, defects are trapped at the front with a strong
coupling between oscillators, similarly to the Kibble-Zurek mechanism in
quenched phase transitions. These defects, which are pinned to the fronts,
yield a strong decay of the correlation length.
