Universal and nonuniversal neural dynamics on small world connectomes: A finite-size scaling analysis

PEROTTI, JUAN I.; CANNAS, SERGIO A.; BILLONI, ORLANDO V.; BILLONI, ORLANDO V.; ZAREPOUR, MAHDI; CHIALVO, DANTE R.; ZAREPOUR, MAHDI; CHIALVO, DANTE R.; PEROTTI, JUAN I.; CANNAS, SERGIO A.

Physical Review E

PHYSICAL REVIEW E

Año: 2019 vol. 100

2470-0045

Evidence of critical dynamics has been found recently in both experiments and models of large-scale braindynamics. The understanding of the nature and features of such a critical regime is hampered by the relativelysmall size of the available connectome, which prevents, among other things, the determination of its associateduniversality class. To circumvent that, here we study a neural model defined on a class of small-world networksthat share some topological features with the human connectome. We find that varying the topological parameterscan give rise to a scale-invariant behavior either belonging to the mean-field percolation universality class orhaving nonuniversal critical exponents. In addition, we find certain regions of the topological parameter spacewhere the system presents a discontinuous, i.e., noncritical, dynamical phase transition into a percolated state.Overall, these results shed light on the interplay of dynamical and topological roots of the complex braindynamics.