  We consider the impact of dynamical dark energy (DDE) in the possible
solution of the existing tensions in the $\Lambda$CDM. We test both interacting
and non-interacting DE models with dark matter (DM). Among the former, the
running vacuum model (RVM) interacting with DM appears as a favored option. The
non-interacting scalar field model based on the potential $V\sim
\phi^{-\alpha}$, and the generic XCDM parametrization, also provide consistent
signs of DDE. The important novelty of our analysis with respect to the
existing ones in the literature is that we use the matter bispectrum, together
with the power spectrum. Using a complete and updated set of cosmological
observations on $SNIa+BAO+H(z)+LSS+CMB$, we find that the crucial triad
$BAO+LSS+CMB$ (i.e. baryonic acoustic oscillations, large scale structure
formation data and the cosmic microwave background) provide the bulk of the
signal. The bispectrum data is instrumental to get hold of the DDE signal, as
our analysis shows. If the bispectrum is not included, the DDE signal could not
be currently perceived at a significant confidence level.
