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Evidence of critical dynamics has been recently found in both experiments andmodels of large scale brain dynamics. The understanding of the nature andfeatures of such critical regime is hampered by the relatively small size ofthe available connectome, which prevent among other things to determine itsassociated universality class. To circumvent that, here we study a neural modeldefined on a class of small-world network that share some topological featureswith the human connectome. We found that varying the topological parameters cangive rise to a scale-invariant behavior belonging either to mean fieldpercolation universality class or having non universal critical exponents. Inaddition, we found certain regions of the topological parameters space wherethe system presents a discontinuous (i.e., non critical) dynamical phasetransition into a percolated state. Overall these results shed light on theinterplay of dynamical and topological roots of the complex brain dynamics.

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