Universal and non-universal neural dynamics on small world connectomes: a finite size scaling analysis

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.