Chimera states in neural networks and power systems

Abstract

Partial, frustrated synchronization and chimera-like states are expected to occur in Kuramoto-like models if the spectral dimension of the underlying graph is low: $d_s < 4$. We provide numerical evidence that this really happens in case of the high-voltage power grid of Europe ($d_s < 2$), a large human connectome (KKI113) and in case of the largest, exactly known brain network corresponding to the fruit-fly (FF) connectome ($d_s < 4$), even though their graph dimensions are much higher, i.e.: $d^{EU}_g\simeq 2.6(1)$ and $d^{FF}_g\simeq 5.4(1)$, $d^{\mathrm{KKI113}}_g\simeq 3.4(1)$. We provide local synchronization results of the first- and second-order (Shinomoto) Kuramoto models by numerical solutions on the FF and the European power-grid graphs, respectively, and show the emergence of \red{chimera-like} patterns on the graph community level as well as by the local order parameters.