Brain function require the control of inter-circuit interactions on time-scales
faster than synaptic changes. In particular, efficiency and direction of
influence and communication between neural populations (described by the
so-called directed functional connectivity) must be reconfigurable even when
the underlying structural connectivity is fixed. Such influences can be
quantified through time-series analyses of time-series of neural activity (such
as Transfer Entropy). But how can manifold functional networks stem from fixed
structures? Considering model systems at different scales, from neuronal
cultures to motifs involving few brain areas and up to brain-wide
thalamocortical networks, we show that ``function and information follow
dynamics'', rather than structure. Different dynamic states of a same
structural network, characterized by different synchronization properties, are
indeed associated to different directed functional networks, corresponding to
alternative information flow patterns (functional multiplicity). At the same
time, different structural circuits generating very similar dynamics can give
rise to equivalent functional networks (structural degeneracy).
Here we show how it is possible, taking into account switching between
collective states of the analyzed circuits, to provide a picture of directed
functional interactions in agreement with a ``ground-truth'' description at the
dynamical systems level. We put then particular emphasis on explaining how
multi-stability between attractors in a subcritical dynamical regime might
account for empirically observed structured patterns of non-stationarity in
resting-state BOLD functional connectivity.