Synchronization and criticality on connectome graphs

The criticality hypothesis for neural systems proposes that optimal information processing, sensitivity, and memory capacity occur near criticality. We investigate the synchronization transition of the Shinomoto-Kuramoto (SK) model on fruit-fly and human connectomes, showing
nontrivial critical behavior with continuously changing exponents, frustrated synchronization,
and chimera states in the resting state [1, 2, 3]. By numerical solution, we determine the
crackling noise durations with and without thermal noise, and show extended non-universal
scaling tails characterized by the exponent 2 < τ < 2.8, in contrast with the Hopf transition
of the Kuramoto model, without the force τ = 3.1(1). Comparing the phase and frequency

[1] G. Odor and J. Kelling, Critical synchronization dynamics of the Kuramoto model on connectome
and small world graphs, Scientific Reports 9 (2019) 19621.
[2] G. Odor, J. Kelling, G. Deco,The effect of noise on the synchronization dynamics of the Kuramoto
model on a large human connectome graph, Neurocomputing, 461 (2021) 696-704.
[3] Geza Odor, Gustavo Deco and Jeffrey Kelling,ifferences in the critical dynamics underlying the
human and fruit-fly connectome, Phys. Rev. Res. 4 (2022) 023057.
[4] Géza Ódor, István Papp, Shengfeng Deng and Jeffrey Kelling, Synchronization transitions on
connectome graphs with external force, Front. Phys. 11 (2023) 1150246.
order parameters, we find different transition points and fluctuations peaks as in the 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 [4]. Our findings suggest that these exponents are smaller in the excited system than in
the resting state and exhibit module dependence.