Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs


Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

Ódor, G.; Kelling, J.

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 804092 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d<4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law--tailed synchronization durations, with τt≃1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τt≃1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1<τt≤2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

Keywords: networks; brain; synchronization; kuramoto model

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Permalink: https://www.hzdr.de/publications/Publ-28952
Publ.-Id: 28952