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Desynchronization dynamics of the Kuramoto model on connectome graphs
Ódor, G.; Kelling, J.;
The time dependent behavior of the Kuramoto model, describing synchronization, has been studied numerically on small-world graphs. We determined the desynchronziation behavior, by solving this model via the 4th order Runge-Kutta algorithm on a large, weighted human connectome network and compared the results with those of a two-dimensional lattice, with additional random, long-range links. In the latter case a mean-field critical transition is expected and here we provide numerical results for the synchonization/desynchonization duration distributions. We find power-law tails, characterized by a critical exponent τd≃1.6(1). In case of the connectome we assumed a homeostatic state, by the application of normalized incoming weights. 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 desynchronization durations, with τt≃1.2(1), away from experimental values for the brain. Additionally, we changed the signs of outgoing weights of 20% of randomly selected nodes, to mimic a model with inhibitory interactions. In this case the at the crossover point we found τt≃1.9(2), which is in the range of human brain experiments.
Keywords: networks, brain, synchronization, kuramoto model
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Publ.-Id: 28952 - Permalink