  Evidence of critical dynamics has been recently found in both experiments and
models of large scale brain dynamics. The understanding of the nature and
features of such critical regime is hampered by the relatively small size of
the available connectome, which prevent among other things to determine its
associated universality class. To circumvent that, here we study a neural model
defined on a class of small-world network that share some topological features
with the human connectome. We found that varying the topological parameters can
give rise to a scale-invariant behavior belonging either to mean field
percolation universality class or having non universal critical exponents. In
addition, we found certain regions of the topological parameters space where
the system presents a discontinuous (i.e., non critical) dynamical phase
transition into a percolated state. Overall these results shed light on the
interplay of dynamical and topological roots of the complex brain dynamics.

Disordered Systems and Neural Networks;Adaptation and Self-Organizing Systems;Physics and Society