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

What makes us humans: Differences in the critical dynamics underlying the human and fruit-fly connectome

“…This renormalization has been used in previous connectome studies [40,41,51,52,66]. Recently, a comparison of modeling and experiments arrived at a similar conclusion: equalized network sensitivity improves the predictive power of a model at criticality in agreement with the fMRI correlations [66].…”

“…In case of a representative of large human white matter connectomes [39] the N = 804 092 node KKI-18 network GP-s have been found via measuring the desynchronization times of local perturbations [51,52]. Now we extend this kind of investigation via Kuramoto model (KM) on the FF connectome.…”

“…Generally we used the Runge-Kutta-4 integration algorithm with step sizes δ = 0.01 or δ = 0.1 if it was sufficient, via a special, parallel algorithm, running on GPU-s. We have averaged over the solutions for thousands of different initial self-frequencies, chosen randomly from Gaussian distributions with zero mean and unit variance at each control parameter value. In a previous paper [52], we have shown the possibility of rescaling these onto more realistic, narrow banded frequencies thanks to the Galilean invariance of the KM. Some of the runs, especially for larger couplings K ≥ 3 , were tested by the adaptive solver Bulrisch-Stoer [65] of the boost library.…”

“…The distribution looks wider, but this is just the consequence of the horizontal rescaling. Finally, we also performed measurements for the desynchronization times as in [51,52]. To define desynchronization "avalanches" in terms of the Kuramoto order parameter, we can consider processes, starting from fully de-synchronized initial states by a single phase perturbation (or by an external phase shift at a node), followed by growth and return to R(t x ) = 1/ √ N , corresponding to the disordered state of N oscillators.…”

“…One of the most fundamental models showing phase synchronization is the Kuramoto model of interacting oscillators [47] and was used to study synchronization transition on various synthetic and connectome graphs available [48][49][50][51][52]. Note, that the Kuramoto equation, while neglecting the integration feature of spiking activity of neighboring neurons, still provides a fundamental, mechanistic model for synchronization transition and criticality.…”