The Effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph

We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph. We determined the dynamical behavior of this model by solving it numerically in an assumed homeostatic state, below the synchronization crossover point we determined previously. The de-synchronization duration distributions exhibit power-law tails, characterized by the exponent in the range 1:1 < st < 2, overlapping the in vivo human brain activity experiments by Palva et al. We show that these scaling results remain valid, by a transformation of the ultra-slow eigenfrequencies to Gaussian with unit variance. We also compare the connectome results with those, obtained on a regular cube with N ¼ 106 nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space.The work has been performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme; in particular, G. Ó. gratefully acknowledges the support of Center for Brain and Cognition Theoretical and Computational Group Universitat Pompeu Fabra/ ICREA Barcelona and the computer resources and technical support provided by BSC Barcelona. Support from the Hungarian National Research, Development and Innovation Office NKFIH (K128989), the Initiative and Networking Fund of the Helmholtz Association via the W2/W3 Programme (W2/W3-026) and the Helmholtz Excellence Network DCM-MatDNA (ExNet-0028) is acknowledged