Synchronization transitions on connectome graphs with external force

We investigate the synchronization transition of the Shinomoto-Kuramoto model Q21
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 < τ_t < 2.8, in contrast with the Hopf
transition of the Kuramoto model, without the force τ_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 β (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.