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 < tit < 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 1/4 106 nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study extends the investigation of the Kuramoto model with additive Gaussian noise on the KKI-18 large human connectome graph, and numerically determines the dynamical behavior of the model in an assumed homeostatic state. The desynchronization duration distributions exhibit power-law tails with exponent overlapping in vivo human brain activity experiments, and scaling results remain valid with a transformation of ultra-slow eigenfrequencies to Gaussian distribution. Comparisons with results on a regular cube with 106 nodes show that internal frequencies can cause frustrated synchronization scaling in an extended coupling space.