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

TL;DR

This study investigates how additive Gaussian noise affects the synchronization dynamics of the Kuramoto model on a large human connectome graph, revealing power-law de-synchronization durations similar to human brain activity.

Contribution

It extends the Kuramoto model analysis to a large-scale human connectome with noise, demonstrating scaling laws consistent with in vivo brain data and comparing with regular lattice models.

Findings

De-synchronization durations follow power-law tails with exponents 1.1 to 2.

Scaling results are robust under frequency transformations.

Connectome and lattice models show different synchronization behaviors.

Abstract

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 $1.1 < \tau_t < 2$, 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 eigen-frequencies to Gaussian with unit variance. We also compare the connectome results with those, obtained on a regular cube with $N=10^6$ nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space.