Synchronization transitions on connectome graphs with external force

Abstract

We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of external excitation. By numerical solution we determine the crackling noise durations with and without thermal noise and show extended non-universal scaling tails characterized by $2<{\tau }_t<2.8$, in contrast with the Hopf transition of the Kuramoto model, without the force ${\tau }_t=3.1(1)$. Comparing the phase and frequency order parameters we find different transition points and fluctuations peaks as in case of the Kuramoto model. Using the local order parameter values we also determine the Hurst (phase) and $\beta$ (frequency) exponents and compare them with recent experimental results obtained by fMRI. We show that these exponents, characterizing the auto-correlations are smaller in the excited system than in the resting state and exhibit module dependence.

11 pages, 12 figures

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