Chimera states in neural networks and power systems

TL;DR

This paper demonstrates the emergence of chimera-like states in neural and power grid networks with high spectral dimensions, supported by numerical simulations on real-world graphs like the European power grid and brain connectomes.

Contribution

It provides numerical evidence that chimera states occur in real-world networks with spectral dimensions below 4, challenging previous assumptions about the necessary conditions.

Findings

Chimera-like patterns observed in European power grid and brain networks.

Numerical solutions show local synchronization and chimera states.

Results suggest spectral dimension influences partial synchronization phenomena.

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.