Synchronization of power systems is not only a vital issue nowadays, but also of major
importance in the development of future smart grids where high penetration of renewable …

The ongoing transition to renewable energy supply comes with a restructuring of power
grids, changing their effective interaction topologies, more and more strongly decentralizing …

Recently there is a surge of interest in network geometry and topology. Here we show that
the spectral dimension plays a fundamental role in establishing a clear relation between the …

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 …

Dynamical simulation of the cascade failures on the Europe and United States (US) high-
voltage power grids has been done via solving the second-order Kuramoto equation. We …

Most models of complex systems have been homogeneous, ie, all elements have the same
properties (spatial, temporal, structural, functional). However, most natural systems are …

The second-order Kuramoto equation describes the synchronization of coupled oscillators
with inertia, which occur, for example, in power grids. On the contrary to the first-order …

Electric power systems during transient states are extensively investigated using variations
of the Kuramoto model to analyze their dynamic behavior. However, the majority of current …

In d> 2 dimensional, homogeneous threshold models discontinuous transition occur, but the
mean-field solution provides 1/t power-law activity decay and other power laws, and thus it is …

Power-law distributed cascade failures are well known in power-grid systems.
Understanding this phenomena has been done by various DC threshold models, self-tuned …