Chimera-like states in neural networks and power systems

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 the case of the high-voltage power grid of Europe (d(s) < 2), a large human connectome (KKI113) and in the 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(g)(EU) (sic) 2.6 (1) and d(g)(FF) (sic) 5.4 ( 1 ), d(g)(KKI113) (sic) 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 chimera-like patterns on the graph community level as well as by the local order parameters.